A "discrete" op amp is simply an op amp built out of individual transistors, caps, resistors, etc, as opposed to op amps contained in an integrated circuit on a chip, such as the 741, TL071, etc. Both accomplish the exact same thing in a circuit; the only reason to use the discrete design rather than a ready-made IC is for an application like the one described in this forum, where the op amp is modified to behave differently from available op amps on the market.
This article covers possibly too much information about op amps; check out the comparator circuit for a pretty clearcut example of the behavior of op amp inputs and outputs:
http://www.uoguelph.ca/~antoon/gadgets/741/741.htmlThis one covers feedback and high level concepts a bit better:
http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opampcon.htmlAlso see the schematic for the Distortion+/DOD-250 over at generalguitargadgets for an example of using an op amp as an amplifier in a simple distortion circuit.