The "near abroad" is the way the Russian politicians refer to the countries that gained independence after the collapse of the Soviet Union; such as Latvia and Ukraine.
They all have a Russian minority (of the Russians who emigrated there when it was a Soviet Republic) and the Citizens of those countries often speak Russian as a foreign or native language.
Also, they often have close ties to Russia, such as trade ties due to both the geographical proximity and to the infrastructure which was established while they were a part of the Soviet Union