The role of miners' strikes in the revolution in Russia in 1991 was significant, as it was one of several key events that contributed to the collapse of the Soviet Union and the emergence of the Russian Federation.
How significant was it? Was it crucial?
Did Yeltzin use miners to acquire power? Did miners benefit from the revolution?
Whether 1991 was a "revolution" or not is a very, very complicated question, and I guess I would say there are points for it and against it. The Soviet political and economic order collapsed, and depending on the location there was popular participation and demonstrations, but at the same time the new political order was largely controlled by people from the very same Soviet nomenklatura, and there were significant continuities. Russia may have become independence in 1991 but it was still under its Soviet 1978 constitution until 1993, for example.
Anyway, specifically with the 1991 miners' strikes, it was actually not very consequential to the course of events leading to the dissolution. For background on the Soviet dissolution, you might want to check out the answer I just posted here.
Specifically for the miners' strikes. The 1991 strikes were a reprise of strikes in July 1989: these had involved miners from Kuzbass (in Siberia), Vorkuta (in the Komi Republic), Karaganda (in Kazakhstan) and in Donbass (which is pretty famous in world news headlines now as being in Eastern Ukraine). These strikes involved 400,000 miners and were the biggest independent labor action in Soviet history. While these began as wildcat strikes, the strikers organized themselves into committees and also coordinated between the different coal-mining areas. While grievances included issues around work conditions and pay, like lack of consumer goods and housing, low pay and inadequate pensions (the coal industry had seen under-investment for years, and inflation was beginning to eat into salaries), a major demand was the wholesale replacement of management. This wasn't necessarily a revolt against the Soviet order per se - over a quarter of the striking miners were Communist Party members (the strikers did tend towards being younger - in their 30s - and better educated miners), and the strikes were framed as being in support of perestroika against corrupt local management, although in Ukraine members of a number of non-communist groups like Rukh and the Ukraine Helsinki Group also participated. Eventually government representatives and the strike committees came to an agreement and genuine democratic elections to local workers' committees were held, which resulted in the replacement or resignation of numerous mine directors. The result of the coalminers' strike had knock-on effects (workers in the metallurgical and chemical industries organized and presented demands, which were acceded to before strikes happened), but the strikes also caused coal delivery shortfalls that further destabilized an already-destabilized Soviet economy.
Continuing political and economic instability (including rising inflation) led to continued dissatisfaction among coalminers, and this led to a second round of strikes in the same regions starting in March 1991 and lasting for two months. This time the strikers began in a much better-organized state than in 1989, and actively sought support from outside groups, notably the "Democratic Russia" coalition that was around and supporting Yeltsin (who by this point was Chairman of the Supreme Soviet of the RSFSR, and had also resigned from the Communist Party of the Soviet Union). The miners in Donbass also coordinated with the non-communist movement Rukh. The strikers' demands were much more explicitly political, demanding Gorbachev's resignation, the dissolution of the Soviet legislature pending new elections, and the transfer of mine ownership to the Soviet republics. Gorbachev attempted to end the strike with offers of a doubling of salaries, but this was turned down by the workers' committees, who did finally suspend strikes in May through negotiations with their respective republican governments.
So how did the 1991 strikes play into the collapse of the USSR? It's actually something of an under-studied area compared to other aspects of the collapse. But even with that being the case, the role of the miners' strikes seems to be indirect, and not central (and so very different from, say, the role of Solidarity in Poland). The strikers' helped republican governments like Yeltsin in Russia and Leonid Kravchuk in Ukraine to strengthen their control of resources against the Soviet center, and provided republican politicians with a basis of popular support in their struggles against Gorbachev. But even then, the strikes had ended in May, and the real precipitating factor was the attempted coup by the Soviet government against Yeltsin on August 19, and Yeltsin's "counter coup" against Gorbachev after the hardliners' failure.
By the way, the 1991 strikes weren't the last miners' strikes in those areas. About 500,000 miners in Russian coalmines (as well as miners in Donbass, now in Ukraine) again went on strike in February 1996 - this time against Yeltsin (and in Donbass, against the Ukrainian government) for hundreds of millions in unpaid back wages. Economic and material conditions had not improved in those coal mines (many of which were heavily polluted and near exhaustion anyway, and not very competitive in a now-global market), and miners ended up feeling very dissatisfied with now the new authorities in Moscow and Kyiv were addressing their grievances. It's not a story that has much of a happy ending, nor does it tidily end with the fall of the USSR.