A testable prediction about the relationship between at least two events, characteristics, or variables. Hypotheses usually come from theories; when planning an experiment, a researcher finds as much previous research on the topic of study as possible. From all of the previous work, the researcher can develop a theory about the topic of study and then make specific predictions about the study he/she is planning. It is important to note that hypotheses should be as specific as possible since you are trying to find truth, and the more vague your hypotheses, the more vague your conclusions.
For example, if I am conducting a study on the effects of different drugs on pain relief, it would be bad to hypothesize that "one drug will have an effect on pain." What the heck does that mean? How can you test to find out if that is true? A better hypothesis might be, "Drug A (whatever that is in that study) will reduce the amount of pain significantly more than Drug B according to participants' ratings of pain using the Pain Intensity Scale."
Related term of interest: Null Hypothesis.