The setting: Parliament can't typically bring bills to the floor for a vote unless the Government (read: the Prime Minister) allows it, much like McConnell or Pelosi. However, unlike our Congress, there are occasions where Parliament can wrest control of the agenda from the Government.

Standing Order 24 wrote some rules around that, one having to do with emergency discussions. The Commons invoked the rule yesterday to attempt to gain control of the agenda to vote on a bill blocking a No Deal Brexit. The vote yesterday was a vote on whether or not to allow that control to be wrested, and it passed because 20 Tory (Conservative) ministers rebelled.

So, that vote passed, which now allows the Commons to discuss and vote on the actual bill to block a No Deal Brexit. That's happening today: The first vote passed and now they're considering amendments, then it goes to the Lords.

The bill itself would require the PM to go to Brussels to ask for an extension of 3 months if the alternative would be to crash out. You're right in that the EU doesn't have to agree but it's very likely they would.