Confidence and supply is an agreement between political parties that is looser than a formal coalition.
A smaller party (or number of parties) makes a deal to back a larger party in government on a vote-by-vote basis, in exchange for policy concessions.
They agree to support the larger party’s budget and other such key votes that would otherwise potentially bring a government down if they didn’t pass. The Queen’s Speech is another example of this. They could also abstain.
This arrangement allows a minority administration to govern without conceding ministerial positions to the junior partner or partners, and in turn, gives smaller parties the opportunity to achieve some of their manifesto commitments without having to sign up wholesale to the leading party’s programme.
The “confidence” applies to the agreement to back the governing party on no-confidence votes, and the “supply” refers to the bills required for the party in power to receive money to enable it to implement its policies. It’s a common misconception that “confidence” means the trust between parties, and “supply” the concessions given to the smaller party/parties.