This isn't really a house rule, it's a variant rule from the DMG. But I'll write down my explanation of how it works.

You can choose two categories of ability check to be proficient in; one is from your background (and you can choose it freely from the six abilities and come up with a way that it makes sense that a baker is good at charisma or whatever).

The other is from your class:

Pro tip! In my five years playing this game so far we've never rolled a Charisma ability check or Constitution ability check. Those are great for saving throws but not for ability checks. The other four abilities are used more often so I recommend that you chose them. It's up to you of course! They're not completely useless: the downtime rules do use those ability checks.

Level two Bard feature. You're just really good at ability checks, you're half proficient in the four you didn't select.

Level seven champion feature. You're half proficient in Strength, Constitution and Dexterity, unless you were already proficient in that ability.

(This ability also boost your jumps but that's unrelated to the whole proficiency issue.)

Level one and six Rogue feature, or level three and ten Bard feature. Your proficiency bonus is doubled for one of the abilities you are proficient in, or for thieves' tools.

(To translate from the old "skill system"; two skill expertises can become one ability expertise.)

(This is a house rule.)

Feat. You gain proficiency in one ability and one tool, or in three tools.