Brain waves

Brain is a three pound organ which contains billions of neurons.
It contains left and right hemispheres each dealing with specific
functions of the body. If the brain has to work, neurons should
communicate each other by using electricity. While millions of
neurons are communicating at the same time, a significant amount
of electrical activity is generated which can be known as brain wave
pattern. Electrical activity originating from the brain is displayed in the form of brainwaves.

Brain waves

Brain waves are oscillating electrical voltages in the brain measuring just a few millionths of a volt. Men, women and children of all ages experience the same characteristic brainwaves.
The brain contains various waves such as beta, alpha, theta, delta,
gamma etc.,

Beta waves - (14-40Hz)

Beta waves are of relatively low amplitude, and are the fastest of the four different brainwaves. They are characteristics of a strongly engaged mind. They are generated when the brain is aroused and actively engaged in mental activities and when the person is consciously alert, feel agitated, afraid and relaxed.  
A person in active conversation, a person making a speech, or a teacher, or a talk show host would all be in beta when they are engaged in their work.
A debater would be in high beta.

Alpha waves - (7.5-14Hz)

Alpha brainwaves are slower, and higher in amplitude. They are characteristics of a relaxed mind and are generated when a person is in physically and mentally relaxed state.
Where beta represented arousal, alpha represents non-arousal.  
A person who has completed a task and sits down to rest, a person who is in meditation state, a person who takes a break from a conference and walks in the garden are in an alpha state.

Theta waves - (4-7.5Hz)

Theta brainwaves, are of greater amplitude and slower frequency. They appear in a deeply relaxed and in a state of somnolence with reduced consciousness.
A person who has taken a break from a task and begins to daydream is in this brainwave state.

Delta waves - (0.5-4Hz)

Delta brainwaves are of the greatest amplitude and slowest frequency. They appear during deep dreamless sleep. If delta waves go down to zero then the brain is said to be dead.

Gamma waves ( above 40Hz) are insight waves. These
waves appear during concentration and problem solving.

All these waves have influence on the cognitive mechanism of the thought processes.
Depending on the activity level of the individual, one brainwave state may predominate at any given time,  while the remaining three brain states are present in the mix of brainwaves at all times.
If a person is in an aroused state, exhibiting a beta brainwave pattern, there also exists in that person's brain a component of alpha, theta and delta, even though these may be present only at the trace level.

The knowledge of the state of brainwaves increases a person's ability to make use of the specialized characteristics of those states, such as being intensely focused, relaxed, creative and restful sleep.