UV-Vis refers to absorption spectroscopy in the uv and visible portion of the electromagnetic spectrum. Light from this region of the spectrum when absorbed by a molecule results in an electronic transition that has two perspectives:
Perspective 1 (from the perspective of the electron): A valence electron (non-bonding or bonding electron) is promoted from the LUMO to the HOMO. The promotion of an electron from one molecular orbital to another results in a charge redistribution within the molecule.
Perspective 2 (from the perspective of the molecule): The molecule changes state. In the ground state, the molecule is usually in a singlet state (a notable exception molecular oxygen). Following absorption of a photon, the molecule will be found in an excited singlet state (due to a selection rule that states a change in electron spin will not occur during an electronic transition).
We can make the connection between electronic transition and absorption spectroscopy by introducing the concept of oscillator strength. The concept of oscillator strength comes from the classical viewpoint that when an an electron bound to a nuclear framework and possesses perfect oscillating properties that the excitation probability of the electron would have an oscillator strength of unity.
If we consider the molecule as a classical oscillating dipole, the probability of an electronic transition is related to the oscillator strength (f), which is defined by the integral over the absorption band:
f = 4.3 x 10^-9 *integral (ε) dν
Here ε is the extinction coefficient and ν is in wave numbers.
I need to clarify one point in my answer that I posted above. The electron promotion need not be from HOMO to LUMO, but more generally from a lower energy molecular orbital to a higher energy molecular orbital. The transition needs to satisfy certain symmetry considerations.