Which enzyme unwinds DNA during replication?

Helicase, which runs along the double helix breaking the bonds between the two strands and prising them apart - and doing so creates a mechanical problem, because unwinding a twisted rope in the middle makes the rest of it wind tighter ahead.

That is solved by topoisomerase, which cuts one or both strands, lets the tension unwind, and rejoins them. The whole replication machine is a set of physical solutions to physical problems: helicase opens, single-strand binding proteins stop it snapping shut, primase lays a starting point, polymerase copies, and because the two strands run in opposite directions one is copied continuously and the other in fragments that are stitched together afterwards.

It runs at about a thousand bases a second in bacteria with an error rate near one in a billion, which comes from proofreading rather than from getting it right first time - the polymerase checks each addition and backs up to remove mistakes. Several antibiotics and cancer drugs work by jamming topoisomerase specifically, which is a good illustration of why understanding a mechanism in that much detail is worth the trouble.