Arbitrageur will know more about this than me, but here's a quick introduction:
As you know, a calendar spread is going long one month versus short another month.
So if March 08 of some contract is quoted bid 93.105 and offered 93.110, and December 08 is quoted 93.470-93.475, then one can immediately go long the March-December spread by going long March at 93.110 and shorting December at 93.470. Alternatively one can short the spread by going short March at 105 and long December at 475.
The exhances recognise this, and take the prices in the outrights to generate implied-out prices from the outrights into the spread quotes. In the above example, there is an implied-out offer for the spread at -0.360 and a bid for the spread at -0.370. In real markets, these bids and offers will be joined by other market participants, and there would usually be a bid or offer at -0.365 in the spread, making it more liquid than the outrights would imply. The main point is that the exchange guarantees that all or no parts of the transaction are executed; if one takes a position in a spread with an implied-out offer then the outrights will trade simulataneously.
The opposite happens with implied-in pricing. Suppose that there were no bids in the December contract, but there was an offer for the spread at -0.360. In this case, a price is implied-in from the spreads into December at 465. If this is hit, then three things will happen: Whoever takes the price will end up with a short position in december at 465, whoever is offering the spread at -0.360 will be at least partly filled, and whoever is bidding for March at 105 will also be filled the number of lots traded by the spread. Implied-in pricing only happens with calendar spreads on LIFFE; I believe that CME also supports implied-in pricing on butterflys.
Finally, there is implied-upon-implied pricing, where implied prices are created from other implied prices. As far as I know no exchanges implement this at all, but there are systems (the previously mentioned autospreaders) that will generate them, although as the different legs of the transaction are not guaranteed there is execution risk.
My experience trading STIRs is that most quoted prices are a combination of implied and, er, "real" prices.