Knowledge is the central topic of the philosophical subdiscipline of epistemology. A good place to begin with this topic is by explaining why most philosophers do distinguish between knowledge on one hand and both truth and belief on the other hand.
Firstly, knowledge is said to differ from truth for the simple reason that not all truths are known; in other words, there are undiscovered truths. Some people (including some philosophers) are apt to respond to this by asking, "What sort of thing is an undiscovered truth?" This is an ontological issue, however, and most of us will probably be satisfied if we simply give examples. For instance, the second law of thermodynamics was already true prior to its being discovered in the 19th century.
Secondly, knowledge is said to differ from belief because we believe many things when we do not really know them.
However, 'knowledge' is very often used in a looser way to refer to any form of truth or belief, a whole body of truth or a whole system of belief. For "knowledge" in this latter sense, see world view, ideology, and religion.
- Some philosophers are even capable of saying that we can have knowledge of a fact without believing it. Cf. Colin Radford, "Knowledge--By Examples." (complete reference needed).