Reply #3: In a parliamentary system...

[liberalpragmatist]

... the prime minister and the cabinet need to have the "confidence" of the majority of the House. That means that a majority backs them or at least won't NOT back them.

Most of the time, this means that a parliamentary majority - either one party or a coalition - will back the prime minister. But in some cases where no party has a majority, the leader of the largest faction will govern in a "minority government" which can stay in power because enough other parties are willing to let them stay in power and won't vote them out of office in a "no confidence" vote. Any legislation that passes will still need the support of other parties in this case, though.

Canada had a minority government until recently. Now, they'll have a conservative majority government.