If two teams played each other once during the regular season (including conference tournaments), they can meet in the third round.
If two teams played each other twice during the regular season (including conference tournaments), they can meet in the regional semifinals.
If two teams played each other three times during the regular season (including conference tournaments), they can meet in the regional championship.
How is this different from last year?
In the past, teams from the same conference were not allowed to meet until the regional finals regardless of how many times they played during the regular season. The exception to the rule was if nine or more teams were selected from a conference—in which case it would otherwise be mathematically impossible to put all of the teams into the eight sub-regions.
What is the impact?
These rule changes pretty much completely scrap last year's policy, perhaps because of how frustrating it was to seed the Big East this past March.
They sent eight teams to the tournament, which meant they had to be equally distributed across each of the eight sub-regions. If any of the teams needed to be moved, it got...complicated.
For example, if Cincinnati was projecting as a No. 9 seed but suffered a loss necessitating a drop to a No. 10 seed, that means they would have to move to a different sub-region—one which was already inevitably occupied by another Big East team.
That other Big East team would then need to be moved whether they deserved a shift or not. If they weren’t placed into the sub-region that Cincinnati came from, it would then impact a third Big East team.
You can probably imagine how much of a domino effect such a move could have under the old rules.
Now, you could theoretically have up to eight teams from the same conference in the same region. They would never actually do that, but don't be surprised if four or five teams from the ACC go to the East region, or if half of the Big 12's representatives compete for the Midwest's spot in the Final Four.
This not only makes it less complicated to build a “legal” bracket, but also increases the flexibility to try to put higher seeds closer to home by not worrying quite as much about a different bracketing rule.