I've always seen Charisma as the more offensive mental stat - that is, the outgoing force of personality, as opposed to the stabilizing force (e.g. Wis). Thus, a person with low Charisma either has little outgoing force of personality, or it is negative, or they haven't much visible personality to speak of.

This means that people are unlikely to pay attention to you when you want them to, or in the manner in which you want them to. They will notice you when you want to be unnoticed, take offense when you want to be polite, and disregard you when you insist on urgency. They will think you're joking when you're serious, and take you far too seriously when you make a joke. They will find you un-funny and unappealing. They will shun you if they can, and ignore you if they cannot.

Consider, for example, that a common housecat has Charisma 7. The little buggers are adorable. However, they have less force of personality than an average human. A cat may be able to get you to do things by gnawing on your leg, or giving you the eyes, or mewling pitifully, or typing in broken English, but it can't make an argument that compels you to act. This of course has nothing to do with its inability to speak.

Cha 3 has a fraction of that force of personality. You couldn't convince a drunk to relieve himself if his bladder were overflowing.

When people refer to Cha 0 being "catatonic," I rule that as having so little force of personality that the character basically ceases to exercise any influence on the world around him. Even an insect has enough personality to act on things; a creature with 0 Charisma simply lacks the agency, the self-governance, to impose his will on the world, because he lacks the outgoing will to impose.

The awkward thing about Cha is how readily it mixes with Wis. It's very hard, for example, to visualize a character with low Cha but high Wis, particularly given how the concept of personality overlaps between the two. (Dr. Sheldon Cooper is an exception, but it can be argued that despite his social awkwardness, he has a very high Cha, as he is able to consistently impose his will on others.) It's much easier to imagine that both Int and Wis are low, and that therefore a person isn't much of a person at all, at least in terms of a person's personality being personable.