1.
extremely large; enormous
An extremely large size or magnitude. Used as a no-adjective to describe something of the greatest possible size.
2.
local maximum; peak value
In mathematics and science, a point where a function reaches a peak relative to nearby values. Also used for the peak of astronomical events like meteor showers.
A compound of 極 (extreme, pole) and 大 (large). Can function as a no-adjective: 極大の.
Usage
Sense 1 (extremely large) is used in general contexts but is fairly formal. Sense 2 (local maximum) is the more common technical usage, appearing in mathematics, physics, and astronomy. In astronomy, 極大 specifically refers to the peak of a periodic phenomenon such as a meteor shower or solar cycle.