Depth is the measure of how deep something goes. The swimming pool has a depth of six feet. The well has an unknown depth. People can be deep as well—you know by looking at some people that they have depth.
Depth goes with other measure words that end in "th." Length is how long something is. Breadth is how wide or broad. The expression "plumb the depths" means to take a measure of how deep something goes. Depth also can mean deepness—your English teacher might instruct you to write papers with depth.