The idea of squeezing arises when discussing the state of a quantum harmonic oscillator (e.g. a bosonic system). Such systems differ from simpler qudit systems in that, even when only a single mode is being considered, the system is infinitely dimensional.
A common way to describe these systems is via pairs of non-commuting observables, often the "position" and "momentum" operators $\hat x$ and $\hat p$. For an arbitrary pair of observables $\hat A,\hat B$, the corresponding uncertainties are bounded by $\sigma_A^2\sigma_B^2\ge\frac14|\langle[A,B]\rangle|^2$.
Whenever a state is such that $\sigma_A<\frac12|\langle[A,B]\rangle|$ (or the same holds for $\sigma_B$) we talk of a squeezed state.
More formally, a squeezed state can be written by having a squeezing operator $$S(\xi)\equiv\exp\left[\frac12(\xi a^{\dagger 2}-\xi^*a^2)\right],\quad \xi\in\mathbb C$$ act on some other state. For example, squeezed vacuum states have the form $S(\xi)|0\rangle$.
The higher the amount of squeezing, the more the uncertainty of one observable is smaller and the other one is larger. This can be pictured in the phase-space representation of the state as a stretching of the function in some direction.
The limit of infinite squeezing corresponds to the uncertainty of one observable being zero and the other one being infinite. Think position eigenstates corresponding to infinite uncertainty over the momentum.
Now, are such states physical? Not really: you can never generate a really infinitely-squeezed state. But one can generate enough squeezing that in a given application you can simplify the model by assuming infinite squeezing. It's just an approximation, which can be useful depending on the circumstances.
See this review to read more about squeezing.
