1.
deep place, depths
A physically deep spot, such as a deep part of a river, pool, or body of water.
2.
depth, profundity, richness
Abstract depth or richness in quality, such as depth of flavor, color, meaning, or character.
Usage
Formed from 深い (deep) + the suffix ~み (which forms nouns indicating degree or quality). The figurative sense (sense 2) is particularly common, used to describe richness or profundity in abstract qualities.
The expression 深みにはまる means both "to step into deep water" literally and "to get in too deep" figuratively.