After the realignment, the league now consists of 2 conferences with 2 divisions in each conference. NHL playoffs consist of 16 teams fighting for the last two spots to compete in the Stanley Cup Final
The way the new playoff structure works is as follows...
The top three teams in each division will make-up the first 12 teams in the playoffs.
The remaining 4 teams (Adding up to 16 teams) will be made up by the next two highest-placed finishers in each conference. Two teams per conference.
This means that the the 2 wild card spots in the Eastern Conference can consist of one of the following:
Two teams from the Atlantic Division
Two teams from the Metropolitan Division
One team from the Atlantic and one team from the Metropolitan.
The way the seeding now works is...
The division winner with the most points in the conference will be matched against the wild-card team with the fewest points
The division winner with the second-most points in the conference will play the wild-card team with the second fewest points.
Here's an example
In the picture below showing the current standings of the Eastern Conference, you can see that the top 2 rows consist of 3 teams for each division. If the season ended today, these 6 teams (3 from the Atlantic Division and 3 from the Metropolitan Division) will make the playoffs.
In the third row, you see a list of every other team in the conference. The top 2 teams in this list are "Wild Card" teams and will also make the playoffs.
The playoff seedings would look like this:
#1 Toronto vs. #8 Boston
(Boston is the wild card team with the least amount of points and will face the team with the most points in the conference which is Toronto)
#2 Pittsburg vs. #7 Tampa Bay
(Tampa Bay is the wild card team with the most amount of points and will face the team with the 2nd most points in the conference)