One of the beauties of a good essay is how much an author can imply or suggest about the theme without directly stating it. This can be done in all kinds of ways. For example:
In analyzing an essay, you want to bring out some of this depth and complexity. Generally speaking, it is not enough simply to point out that the theme is present, though this is obviously the first step. (In some descriptive essays, where the theme is not obvious, pointing out how the author uses physical descriptions to convey deeper ideas may be enough.) Instead, what you want to do is try to see what the author is saying about the theme.
I say "about" because one of the main purposes of a good essay is to explore or develop a theme, much the same way that a piece of music might develop a theme, starting off with a simple statement of the melody, then going off into all sorts of complications and variations, then coming back to the simple melody at the end, but now with a sense of the possibilities it contains. An essay looks at its theme(s) from many angles, giving us lots to think about and helping us see more depths than we might have otherwise. In short, the author states or suggests many different things about the basic theme, and analyzing the essay means bringing out some of those things.
These questions will help you dig deeper into the theme. Often the answer is not stated directly but implied by the story, the description, the facts presented.