brain function

Left hemisphere
Language

Math

Logic

Reasoning

Right hemisphere
Spatial abilities

Face recognition

Visual imagery

Music

In evolutionary terms, lateralization increases the number of different ways the brain can respond to its environment in order to improve chances for survival.
In as many as 90% or more right-handers, the left hemisphere accomplishes most language processing functions. In non-right handers (which include left-handed and ambidextrous people), language functions are far more likely to involve the right hemisphere. There is some evidence that lateralization differs in males and females.
The left hemisphere is the dominant one for right-handed people, due to contralateralization: the left side of the brain controls the right side of the body, and vice versa.

Frontal lobe (pink)
Concerned with reasoning, planning, parts of speech and movement (motor cortex), emotions, and problem-solving.
Includes Broca's area.

Parietal lobe (blue)
Named for the parietal ("wall") bone on the side of the head.
Concerned with perception of stimuli related to touch, pressure, temperature, and pain.

Temporal lobe (green)
Named for the temporal bone at the temple.
Concerned with perception and recognition of auditory stimuli (hearing) and memory (hippocampus).
Includes Wernicke's area.

Occipital lobe (yellow)
Named for the occiput, the protruding bone "at the back of the head."
Concerned with many aspects of vision.