In brief, the theory of Reliabilism in epistemology, states that you know something to be true if and only if: 1) you believe some proposition to be true, 2) that proposition is actually true, and 3) you have arrived at the belief that the proposition is true through some reliable process.
The third clause is generally presented as an alternative to the notion that you must be justified in believing X in order for that belief to be true. Justification is being used here in its standard epistemological sense, to indicate that any belief you hold must be based on strictly upon the evidence available to you in order to qualify as knowledge. The distinction the reliablist makes is that the someone does not need to know that the process she is using to form a belief is a reliable belief formation mechanism, as long as process she uses actually is reliable, she is warranted in calling that belief knowledge. This of course means that reliabilism is based on a controversial claim that at least some of the relationships which are essential to knowledge formation may be external to the consciousness of the person forming the belief.
Philosophers who advocate a form of reliabilism: