What does the notation $G\times_P\mathfrak{p}^\perp$ mean, for $P\subset G$ Lie groups?

Question

Suppose $G$ is a Lie group, $P$ a Lie subgroup with $\mathfrak{p}$ the associated Lie algebra.

What object is $G\times_P\mathfrak{p}^\perp$? I don't understand what the $\times_P$ means, specifically with the $P$ subscript.

It shows up in a geometric context, since apparently $G\times_P\mathfrak{p}^\perp\cong T^\ast(G/P)$, the cotangent bundle. Is it a quotient of $G\times\mathfrak{p}^\perp$ of some sort?