These are draft picks in the 3rd through 7th round awarded to NFL teams who lost high value unrestricted free agents the prior year (this excludes "street free agents"). The actual formula used to determine the type of pick is not known, it's a closely guarded secret. The formula takes into account the lost player's performance, playing time, salary, and honors such as being named to the Pro Bowl.
In the off-season if a team signs more free agents than it loses, that team is not eligible for compensatory picks. Teams that sign and lose the exact same amount, but are deemed to have lost higher value players, are eligible for picks. It's important to note that compensatory picks can not be traded
For example, a team that loses a $4 million a year starting wide receiver might be awarded a 3rd or 4th round compensatory pick, meanwhile a team that loses a $1 million a year corner-back would get a 6th or 7th round pick.
The most compensatory picks that can be awarded by the NFL each year is 32. The league essentially ranks all the free agents lost, teams that lose one of the top 32 players are eligible for a pick. If less than 32 picks are awarded, then the remainder are given to teams in order as if there was an 8th round (the end of the draft).