Central Asia is a region to the south of Russia which consists of Kazakhstan, Uzbekistan, Tajikistan, Kyrgyzstan and Turkmenistan. All five countries are former Soviet republics with different although related languages and mostly unfortunate post-Soviet histories. They were thoroughly integrated into the USSR economy and some people think independence brought them more grief than joy.
Only kazakhs as the largest and the most northern country of the five enjoy a relatively high level of life. The rest consist mostly of desert or mountains which are very expensive to develop. For example Uzbekistan was once blessed with Aral Sea — a huge salty lake rich with fish — which is all but vanished nowadays because of the irrigation efforts needed to grow cotton for the whole USSR.
Weak economy is probably the main reason people try to move to Russia from Central Asia. But not the only. There is a very important language factor. The CIS is a region where a Russian feels like an Englishman or American man in Europe. Central Asia is not an exception. Most people speak Russian in these countries to at least some degree and that allows them to easily communicate in Russia. It is interesting that sometimes the Russian language as spoken by those immigrants is more proper than the one spoken by native Russians. During Soviet times the language and culture were literally exported to the republics by highly intelligent and educated teachers that were sent there to help create schools and the whole educational systems. We now see the results of those efforts reading about Alisher Usmanov, a famous Russian oligarch, one of the richest people on Earth. He was born in rural Uzbekistan.
There were a lot of russian people who moved to the frontier of the warm sunny Central Asia both by and against their own will during Soviet period. There were times when Russians were a dominant nation in capitals of Tashkent and Alma-Ata. Most of these people or their descendants returned to their historical motherland of Russia since 1990s. This is another reason for the immigration — repatriation.
Most of the central asian countries have not developed any form of modern democracy. And while Russia is far from perfect in this particular aspect, many Uzbeks, Tajiks and Turkmens enjoy much more freedom here than in there native countries. Central Asia is infamous for its long-ruling presidents — most have been in office since the USSR demise and been re-elected time after time by changing laws. They even use such titles as the National Leader (Nursultan Nazarbaev) or the Father of All Turkmens (Saparmurat Niyazov, died in 2006). Such atmosphere forces the most educated and knowledgable people to flee their countries to search for a place more suitable for living and raising children.
The stream of Central Asian immigrants is probably the largest source of population increase now in Russia (but the population on the whole is nevertheless on the decline) rivaled only by Chinese immigration in Southern Siberia.