There are two types of portraits: golden and diamond. They function like their counterpart in Constructed, golden and diamond cards: Both give a new, animated look of the mercenary, and diamond gives a 3d animated look and a rainbow SFX when put into battlefield in gameplay.
As all mercenaries have 3 different base portraits, they also have 3 different golden portraits to obtain. Each legendary mercenary will also have 1 diamond portrait, except for Grommash Hellscream (no apparent reason why).