It's tough to come up with a "one size fits all" answer here. Equality generally refers to material and/or positional equality. "=" positions usually have balanced pawn structures (ie 4 Q-side and 3 K-side pawns on both sides) but this is not an absolute rule. In some cases each side might have pawn weaknesses, for example White has doubled QB pawns and Black has an isolated h-pawn. On the other hand "oo" (infinity sign) implies dynamic equality, usually meaning the position is so complex that chances are probably even at least among human beings. "=" usually refers to static equality, ie K+B+4 pawns vs K+B+4 pawns with Bishops of the opposite color for instance.
Equality
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I tried this under Openings but got no replies. When the books talk about Black gaining equality, what exactly do they mean. Is it when White no longer has the initiative from having the first move? This seems like a rather vague concept to me. Would/could anyone please explain equality and when do you know you have it with Black?