A coalition is basically where two or more parties get together to form a majority party. You need a majority in order to form a government (because when you come to vote on legislation you want to be able to get your laws through - any everyone else will probably try and block them)
So after the election if no party has an overall majority (there are 646 seats in the House; so 323 needed to form a majority) then they will look to others parties for support (lib dems, snp, etc).
These parties can then make deals whereby they will form a coalition on the basis of...(they then set out their demands).
The Lib Dems are more likely to go with Labour because they're ideologies are closer.
If the Conservatives are only a couple of seats away from an overall majority (i.e. 320) then they could approach SNP/plaid cymru/independents to form a coalition rather than having to go to the Lib Dems.
Coalitions are really complication - and in this country and generally not good for government. It will mean that it takes a very long time for anything to happen (because deals have to be made); which in a recession is a really bad thing.
Coalitions fall apart quite quickly (because parties are not used to sharing powers) and that is why another election is generally called quickly; especially if a party thinks it could get enough seats for a majority.
Does that make sense - happy to explain further