Are you referring to soviet as in the political body/unit or in more casual sense e.g. a soviet as being shorthand for a Soviet citizen? I'm guessing the former but the wording of your question is odd.

In answer to the question of the soviet as a political unit, you're essentially looking at the Supreme Soviet (larger body, meeting rarely) and its Presidium (sub set of the Supreme Soviet, meets more regularly). In terms of raw power this institution was pretty marginal - the party based Politburo and the state based Council of Ministers in practice set and implemented policy. The soviet was more a formal institution and a bit of a 'rubber stamp'.

That being said the Supreme Soviet was from time to time used as a platform for grievances and concerns about the state. So it could be one opportunity to be heard for some.

Under Gorbachev this was revamped and the Soviet became essentially a counter force or alternative to the party.