FIDE have just taken the decision to exclude teams from Russia and Belarus in any official FIDE team competition, at least for the foreseeable future. The most obvious effect of this decision is that both countries will not be able to take part in the upcoming chess Olympiad. This decision does not effect individual players, although in that case, the players themselves are required to play under the FIDE flag (or change federations).
In terms of how this effects the Olympiad itself, the loss of the Russian team does make it a little easier for other countries. However it is worth noting that Russia last won the Olympiad in 2002, while countries like Armenia, China and Ukraine have won it multiple times since. Of course the previous incarnation of the Russian team, the USSR, was absolutely dominant, winning every Olympiad from 1952 to 1974, and then again from 1980-1990. In that era they were able to draw on players from other republics, including Ukraine.
One of the players from the early years of the Soviet Olympiad team was David Bronstein, considered one of the most original thinkers in the game, and one of Ukraine's greatest players. Here is a game from his first Olympiad, against Henry Grob, who missed the chance to play his own opening (1.g4).
Grob,Henry - Bronstein,David I [B23]
Helsinki ol (Men) prel-C Helsinki (2), 1952