A situation where the movement of the opponent's pieces gets more and more restricted as the attack develops. The opponent can't make moves easily without losing something.
As @Ywapom notes, Zugzwang is often used to the describe the end of this situation, like the Immortal Zugzwang Game where Sämisch suffers this fate against Nimzowitsch.
For the progress itself, it's perfectly normal to use non-chess specific terminology here, e.g. you could say White was slowly getting strangled by Black in the game above.
It sounds like you are describing near "zugzwang". "Zugzwang: a situation in which the obligation to make a move in one's turn is a serious, often decisive, disadvantage" https://en.wikipedia.org/wiki/Zugzwang
"Bind" is another term often used to describe restriction.
If every single one of the opponent's moves loses something, then he is considered to be in zugzwang. However, if he has a position where it's simply difficult to find a satisfactory move, then he would be considered suffocated, cramped, or even squeezed.
There's no official/accepted term for general restriction of your opponent's pieces, but any of the 3 I mentioned above are expressions which are commonly used. However, zugzwang is the official/accepted term for a position where all moves lose.