I've not had much to do with scheduling, but what often happens if an airline operates more than one flight a day is that the lare arrivinf inbound crew will operate an early afternoon flight the following day and the crew from that will leave early the following morning. This means that the airline has to pay for rooms for two sets of crews. Stabling away from base is expensive but worth it commercially. The alternative as the last post says is the standover day. This explains why if you have serious disruption such as fog on one days you will often get cancellations on the following day (or in bad cases days).
With a Europen legacy short haul rosters may comprise three flights on day 1 (such as LHR-GVA-LHR-ZRH) and then day 2 might be ZRH-LHR-BSL-LHR (a made up example). Patterns might be longer lasting several days. European low cost carriers are much more out and back as because they have bases in several countries there is much less need to outbase staff - it is also one reason why their costs are lower. American carriers can have very complex patterns.