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Antenna Pattern in details
Antenna pattern is a three-dimensional distribution of antenna intensities during the transmission of electromagnetic waves.  The antenna patterns varies significantly for directional vs. Omni-directional antennas.  Theoretically 3D (three-dimensional) pattern can’t be examined so  techniques to extract 2D (two-dimensional) patterns is employed.
We can extract slices in 2D from the 3D patterns. The different techniques of extracting slices are listed below.
Azimuth pattern (AP) - A slice from horizontal view crossing the center.
Elevation pattern (EP) - A slice from vertical view crossing the center.

The azimuth and elevation patterns are 2D version of 3D actual antenna pattern. For directional antennas the AP and EP will look more likely ellipse whereas the omni-directional will look like circular pattern.
An important parameter in characterizing the antenna pattern in Beam Width.
Beam width is an angular measurement of power strength in a particular direction.  

Beam width is also 3D quantity and can be broken into 2D parameters.

The beam width of an omni-directional pattern is 360° since the power is equal in all directions.

The beam width for directional pattern will always be lower than 360° since the power is concentrated in some particular direction.
Antenna Pattern and Beam width discussion.
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