Binaural beats are the playing of two sine waves of close, but not the same, frequency into different earpieces of a set of headphones. The "beat" is heard as the brain tries to process them as a distinct sound, while taking into account the constructive/destructive interference. It is said to migrate brain waves to be closer to that frequency, like a sort of biological resonance, which is true. Of course the same can be said for listening to relaxing music help you relax, up tempo music to help you feel energetic, etc...

With regard to listening without headphones specifically, you might find it irritating if you are someone who suffers from motion sickness, depending on how the track is created. If you were listening to binaural beats, they really need headphones to work properly. If you are in a room and closer to one speaker you may not even hear binaural beats properly, and if sitting off centre in the room generally, that may have unsettled you if you have motion sickness as the tones try to form a beat in your head. If it was just a standard isochronic tones theta track that shouldn’t be irritating if you have motion sickness.

When stress overwhelms your nervous system, your body is flooded with chemicals that prepare you for “fight or flight.” This stress response can be lifesaving in emergency situations where you need to act quickly. But when it’s constantly activated by the stresses of everyday life, it can wear your body down and take a toll on your emotional and physical health.

This can help develop the ability to see energy fields around people and in nature, and it will also make it much easier to stay awake during your meditations. When your eyes begin to close, you simply have to open them back up again. Doing the meditations with your eyes open is a serious step up in exercising your brain, so go slow with that technique at first.
It may be that you had the volume too loud, but I would expect you to hear the effects of that straight after you’ve stopped listening, not on a day you haven’t used them. It might be something similar to muscle memory, where you suddenly remembered the sound and sensations it gives you as if you were hearing it again. I don’t know how long you’ve been using this type of thing for, but maybe it’s something that will settle down and disappear once you become more accustomed to the sound.

Acupuncture has increasingly been used to treat many stress-related conditions, including psychiatric disorders, autoimmune or immunological-related diseases, infertility, anxiety, and depression. Researchers have found that acupunture treatments result in changes in the cardiovascular and immune systems, increasing protective T-cell proliferation and helping with cellular immuno-responses. (8)

From a strictly physical/emotional viewpoint, the benefits of meditation include (but are not limited to) such things as greater resistance to stress; less physical illness and improved resilience when illness does occur; better quality of sleep and increased recovery during sleep; a generally magnified sense of well-being; a sharper, clearer mind; increased capacity for learning; improved functioning in daily life; more harmonious relationships; greater control over emotional states, and more.
Alpha Waves (7-13hz) are associated with light meditation, peak performance, creativity and relaxed alertness. Your brain goes into this state naturally when you are daydreaming. Alpha waves also become more predominant when you close your eyes and relax your mind. This is the perfect state to be in for subliminal mind programming and enhancing your creativity.
Go behind the scenes of brainwave entrainment technology creation with Joseph Kao, developer of the extraordinary meditation tool Journey to the Center of the Self. Here, in an interview with John Dupuy, CEO of iAwake Technologies, Joe describes the amazing complexity of the brainwave entraining soundscape he created to both accompany his deeply inductive, 30-minute, guided meditation on the first track of Journey, and also stand alone as a music-only track that holds you in a profoundly relaxed, still, yet clear place on the theta/delta border. To find out all that went into the making of the inductive guided meditation on the first track of Journey, see A Guide to Transpersonal Meditation: Journey to the Center of the Self, part I of this interview.
Other entrainment methods sometimes used include autopan modulation that moves sound in an 180º arc to create a desired tone. Harmonic box entrainment, invented by James Mann, uses a layering of binaural and monaural tones that alternate between ears, requiring headphones. Sound modulation and filtering, amplitude modulation, and pitch panning use diverse sounds to create rhythmic pulses matched to the desired brainwave frequency. 
Science shows that massages reduce stress, but you don’t have to go to the spa—you can give yourself one right now. “Learning how to self-massage your foot, head, neck, or shoulders reduces the stress hormone cortisol, boosts your immune system, and increases the feel-good hormones oxytocin, dopamine, and serotonin,” Dr. Serani says. You can even use a tennis ball or cold water bottle on your feet or neck. In addition, try rubbing pressure points like the webbing between your thumb and index finger, or your inner wrist. Another technique is the EFT tapping technique, literally tapping certain points on your body such as in between your eyes, your temples, and the center of your collarbone. “Tapping brings cleansing energy to the meridian points, as your mind directs the energy to what’s unbalanced in the body,” Whitaker says. “This restores your mind and body’s natural balance, which aids in releasing stress, worry, fears, and disharmony.”
In one study, researchers had a group of participants relax alone in a quiet, low-light environment following an exercise session. They split the group in two — one spent 20 minutes listening to theta-frequency binaural beats while the other listened to a carrier tone and monitored their parasympathetic (rest and relaxation) and sympathetic (fight or flight) nervous system activity. Researchers found the group that listened to binaural beats experienced an increase in parasympathetic activity and a decrease in sympathetic activity, along with higher rates of self-reported relaxation.
Tracks that move from alpha to theta can be a perfect vehicle for transitioning from a hectic day into a relaxing and rejuvenating sleep. Beginning with alpha waves takes you into a light but still alert meditative mind state where the difficulties of the day can be resolved and put to rest. Later, theta waves go deeper into the unconscious, preparing you for sleep and dreams.
You may recognize the "binaural recording" from ASMR, where the technique is often used. This explains why, if you search for "binaural" on YouTube, you get a mixture of two entirely different kinds of results: binaural beats and binaural ASMR recordings. It gets especially confusing in that there's some questionable and/or unexplored science surrounding each one.
This version of Theta Waves music is nice to listen to and the theta wave with binaural feeding of different wave lengths might be correct as the author indicates it, but for me it was disturbing that in the general sound track of a constant gliding sound I expect from Theta Healing CDs some ringing sounds like bells constantly interfered just in moments when the brain and mind would go into the meditation state and synchronize both sides of the brain. As I am a musician myself and use a lot of classical music but never normally use music for meditation, I felt a bit disillusioned from this CD. For the purpose of Theta Healing and deep Theta Meditation, I would not use this music, but prefer the Theta Healing CDs. I was really astonished that so many people say they can meditate deeply with this music. Perhaps my brain is somehow different. I asked myself if the author ever has experienced what a deep meditation with no thoughts and complete stillness is. Music is also able to distract us from true meditation and this kind of music does.
If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.