In I.3 of these notes: https://www.math.arizona.edu/~swc/aws/2005/05SchnepsNotes.pdf Schneps defines a homomorphism
$$G_{\mathbb{Q}}\rightarrow \operatorname{Out}(\widehat{F_2})$$
and states that the inertia groups are $\langle x\rangle, \langle y\rangle, \langle z\rangle$. Here $x, y, z$ correspond to the loops going around $0, 1, \infty$ in the fundamental group of $\mathbb{P}^1-\{0, 1, \infty\}$, of which $\widehat{F_2}$ is the profinite completion of.
My question is, in what sense are these "inertia groups"? And why does this imply the next line, in which Schneps gives a lifting of the outer action by
$$\sigma(x) = x^\alpha, \sigma(y) = g^{-1}y^\beta g, \sigma(z) = h^{-1}z^{\lambda}h?$$