Brain wave patterns can be called waveforms or frequencies. They occur at different frequencies (cycles /second or Hertz), some fast, some slow. The main frequency bands are called beta, alpha, theta and delta.
BETA Brainwaves or Frequency Bands

Small, faster brainwaves.
Low beta: 13-18 cycles/sec. or hertz. Necessary for mental/intellectual activity, good memory, scholastic, athletic and job performance excellence.
High beta: 18-36 cycles/sec. Can create symptoms of Hyper-arousal or anxiety.
ALPHA Brainwaves or Frequency Bands

Slower and larger brainwaves.
8-12 cycles/sec.
Relaxation and idling state. Brain is getting ready to work or slow further toward sleep.
THETA Brainwaves or Frequency Bands

Slower and larger brainwaves
4-8 cycles/sec.
Day-dream, spacey, deep hypnotic or meditative state.
Often seen in ADD/ADHD, learning problems, brain injury, poor mental function, a wandering mind, difficulty focusing, concentrating, poor memory and other symptoms..
DELTA Brainwaves or Frequency Bands

Slower and larger brainwaves
1-4 cycles/sec.
Associated with sleep.Foggy brain if seen in the awake state.
“When an excessive amount of slow waves are present in the executive {frontal) parts of the brain, it becomes difficult to control attention, behavior and/or emotions…..Such persons generally have problems with concentration, memory, controlling their impulses and moods or with hyperactivity. They can’t focus very well, are distractible and exhibit diminished intellectual efficiency.” Hammond, D. Corydon, PhD, What is Neurofeedback? Journal of Neurotherapy. Vol 10(4)2006, p. 26.