My belief that I am conscious is considered by many to be self-evident; your belief that I am conscious is not.
In informal or colloquial speech, "self-evident" often merely means "obvious."
Certain forms of argument from self-evidence are considered fallacious or abusive in debate. An example is the assertion that since an opponent disagrees with a (claimed self-evident) proposition, that he must have misunderstood it.
It is sometimes said that a self-evident proposition is one whose denial is self-contradictory. It is also sometimes said that an analytic proposition is one whose denial is self-contradictory. But these two uses of the term self-contradictory mean entirely different things. A self-evident proposition cannot be denied without knowing that one contradicts oneself (provided one actually understands the proposition). An analytic proposition cannot be denied without a contradiction, but one may fail to know that there is a contradiction because it may be a contradiction that can be found only by a long and abstruse line of logical or mathematical reasoning. Most analytic propositions are very far from self-evident. Similarly, a self-evident proposition need not be analytic: my knowledge that I am conscious is self-evident but not analytic.