In Major League Soccer, the Designated Player Rule is commonly defined as a rule that:
"Allows each MLS franchise to sign players that would be considered outside of the team's salary cap (either by offering the player higher wages or by paying a transfer fee for the player), allowing MLS teams to compete for star players in the international soccer market." - Wikipedia (emphasis added by me)
So in principle, this rule is to do two things: 1) give MLS clubs the capacity to sign big-name players, and 2) sign them in a way that still gives you cap flexibility to build a proper team around said star.