Hi,
prereouting: call comes in, hits ICM, script is run, telling the routing client (PSTN) where to route the call to (so the call is routed before (pre-) connection, or rather, establishment).
Postrouting: call comes in, is connected and then it hits ICM (so the call is routed after begin connected).
Translation routing is an interesting hybrid: call comes in, is connected but the party the call is connected to, is being monitored by ICM (so it sends the call away but it keeps an eye on it). When it's necessary, call is transferred to a different destination.
Examples:
Prerouting: PSTN -> ICM (script) -> PSTN -> destination phone answers
Postrouting: PSTN -> call is answered -> ICM -> transfer to destination phone, answered
Translation routing: PSTN -> call is answered -> ICM transfers to IVR port, then transfers to final destination phone (agent).
G.