Sure, the thinking behind it is reasonable. The idea is that recessions naturally increase government borrowing, by increasing spending on unemployment benefits, and by reducing tax revenues. But how can we be sure that this is the only reason why government is borrowing? This is where the structural budget deficit comes in. It is the amount the government would borrow, if the economy were operating at its trend level.
To measure it, we first estimate how far output is below its trend level - the output gap. Then we estimate the sensitivity of taxes and spending to GDP. We then multiply these sensitivities by the output gap. The structural budget deficit drops out.