This is probably a silly question but here goes!

I have a council allotment with heavy clay soil (two spade depths down and
it's pure yellow-orange clay). Also, the soil structure has been ruined due
to heavy equipment on the plot.

I've built raised beds and done my best with what I have, but now I'd like
to enrich the soil and improve its structure.

I have 2 compost heaps on the go, but they won't be ready for months. I
also have a huge pile of manure but, again, it won't be ready until next
September.

Gardening advice is to add lots of "well-rotted manure or compost" to the
soil but what, exactly, is "compost"? Is it the multi-purpose stuff you can
buy in big bags from B&Q, etc?

Thanks.