Solving a numbers problem
The inverted full-back tactic moves a defender into central midfield when their team has possession, rather than keeping them wide as an overlapping option. The purpose is numerical: it gives the team an extra passer in the centre of the pitch without sacrificing a winger or striker to do it, which matters against opponents who press aggressively in wide areas and leave central spaces comparatively open. Played well, it turns a full-back into a auxiliary midfielder for phases of the game while a winger stays high and wide to stretch the pitch instead.
Why it appeals against a press
Teams that face heavy pressing in wide areas often struggle to build attacks because the touchline reduces their passing options to begin with, and a full-back pinned against it has nowhere to go under pressure. Bringing that player inside gives them passing lanes in both directions and makes the press harder to organise, since the opposition now has to decide whether to follow a defender into central midfield or leave them unmarked there. It is a specific answer to a specific problem, which is why not every team uses it and why it is not simply an upgrade on traditional full-back play.
The gap it leaves behind
The obvious cost is that the wide defensive area the full-back used to occupy is now empty, and if possession is lost quickly, the opposition can attack directly into that space before the team has reorganised. This is why inversion is usually paired with a specific plan for transition, such as a covering midfielder or a centre-back comfortable shifting wide temporarily. Teams that adopt the tactic without solving that problem tend to look excellent in possession and vulnerable exactly when the ball changes hands, which is often the moment matches turn.