Used when two parties are even, especially after settling a debt, score, or mutual favor. Often in the phrase おあいこにする (to call it even).
Let's call it even with this.
You treated me last time, so now I'll treat you and we'll be even.
From 相子 (あいこ, 'even, quits') with the polite prefix お. The kanji 相 means 'mutual' and 子 is a nominal suffix, but the exact derivation is uncertain.