The most frequently asked question people have about this sort of thing is, "what's a jet generation." Simple, it's just the periods during which jet fighter technology made major advances. Thus the first generation jet fighters were those produced during World War II and through the late 1940s. The best examples of these are the U.S. F-86 and the Russian MiG-15. The second generation got going in the early 1950s, and produced aircraft like the U.S. F-104 and the Russian MiG-21. The third generation followed within a decade, producing the U.S. F-4 and the Russian MiG-23. The fourth generation arrived in the 1970s and 80s with the F-15, F-16, F-18, Russian MiG-29, Su-27 and French Mirage-2000. The fifth generation includes the F-22, F-35, and whatever the Russians come up with. The Eurofighter and Rafael are often called Generation 4.5. Russian fifth generation fighter developments were halted when the Soviet Union disintegrated in 1991. Actually, all development work on new fighters, by everyone, slowed down in the 1990s. But work on the F-22, F-35, Eurofighter and Rafael continued, and those aircraft became, in roughly that order, the most advanced fighter aircraft available today.
The new Russian aircraft will have to provide some big advances in electronics or stealth to earn a place in the fifth generation. Otherwise, the Russians are just developing more generation 4.5 aircraft. But if the Russians can provide inexpensive new fighters, they will find a market for them.
China is also taking a stab at developing a fifth generation fighter. But given the state of their current technology, and the rate at which their aviation manufacturing capabilities are progressing, it is more likely that the Chinese will be contenders for the Sixth Generation (which will probably be unmanned.)
Russia has now decided that it will fund only one fifth generation fighter project. Over the Summer, the government announced it would pay for the development of two fifth generation fighters, to compete with the American F-22 and F-35. The MiG company was to develop a "light" fighter (roughly comparable with the U.S. F-35), while the Sukhoi company developed the heavier (F-22 class) fighter. A new, thrust vectoring, version of the AL-41F jet engine is being developed for these fighters. New electronics systems are under development as well. Now the MiG company has been told that they will not receive any government development funds. The MiG project can continue, but MiG will have to pay for it until something impressive enough is produced, that will encourage the government to kick in some financial support.