A hypothesis is either a suggested explanation for an observable phenomenon, or a reasoned prediction of a possible causal correlation among multiple phenomena. In science, a theory is a tested, well-substantiated, unifying explanation for a set of verified, proven hypotheses. A theory is always backed by evidence; a hypothesis is only a suggested possible outcome, and is testable and falsifiable.
edit Examples of Theory and Hypothesis
Theory: Einstein's Theory of Relativity. This is a theory because it has been tested innumerable times, verified, and the result invariably only verifies the conclusion.
Hypothesis: If a prisoner learns a work skill while in jail, it is less likely that she will commit a crime when released. This is a hypothesis, because it just makes sense to the logical mind, but there's no evidence this will happen time and again with exactly the same result.
This video further explains the difference between a theory and a hypothesis:
edit Common Misconception
People often tend to say "theory" when what they're actually talking about is a hypothesis. For instance, "Migraines are caused by drinking coffee after 2 p.m. - well, it's just a theory, not a rule."
This is actually a logically reasoned proposal based on an observation - say 2 instances of drinking coffee after 2 p.m. caused a migraine - but even if this were true, the migraine could have actually been caused by some other factors.
Because this observation is merely a reasoned possibility, it is testable and can be falsified - which makes it a hypothesis, not a theory.