LONDON — Millions of Brits go to the polls Thursday, in an election likely to oust the Conservative Party that has dominated postwar politics and ruled the United Kingdom for the past 14 years.

Who governs Britain should matter to Americans. The U.K. is considered Washington’s closest ally, it is the world’s sixth largest economy, and it has a nuclear arsenal and a permanent seat on the United Nations Security Council.

Here’s what to know about this pivotal vote.

The big picture

This…