Why did he commit suicide ...
It was clearly suicide by SEAL.
(The SEAL team shoots out the lock on the final door with a shotgun and proceed into the room. The room is empty except for Vadim Tarasov at the head of the table with a Beretta 92FS on the table in front of him.)
TARASOV: Every man has an end. I'm fine with this one.
SONNY: So am I.
(Tarasov reaches for the gun and Sonny shoots him once in the forehead, dropping him dead where he sat.)
Image courtesy of IMFDB
He didn't want to go to prison/Guantanamo/The Hague. While not directly parallel, the situation is analogous to suicide by cop.
There are two broad categories of "suicide by cop". The first is when someone has committed a crime and is being pursued by the police and decides that they would rather die than be arrested. These people may not otherwise be suicidal but may simply decide that life is not worth living if they are incarcerated and thus will provoke police to kill them. The second version involves people who are already contemplating suicide and who decide that provoking law enforcement into killing them is the best way to act on their desires. These individuals may commit a crime with the specific intention of provoking a law enforcement response.
... and why did the Seals want him?
Bravo Team is in Serbia to track down an organization linked to the bombing of multiple American military outposts. The man behind the organization was believed to be Vadim Tarasov who now becomes an HVT (High Value Target aka whale). He was located after Bravo Team captured Peter Malkin at a small airfield. Malkin was a businessman who ran a money exchange known for illicit ties to Tarasov. He gave up information on Tarasov after CIA officer Mandy Ellis threatens to 'leak' false reports of CIA payments to Malkin over the last two years. This information leads them to a villa in the Accursed Mountains in Albania.
BTW, it's Vadim Tarasov (played by Milan Milosevic), not Vadim Tasarov as reported by IMFDB.