A tete-a-tete might be a casual chat, but it's more likely to be a formal conversation or meeting between only two people.
If your boss requests a tete-a-tete with you, she means that she wants to have a meeting, just the two of you. Maybe you'll get a raise at the tete-a-tete — or maybe you're in trouble. You could schedule a tete-a-tete with your college adviser or plan to sit down with your roommate and have a tete-a-tete about the dirty dishes in the sink. The leaders of warring countries might also try to settle disputes through a tete-a-tete. In French, tête-à-tête literally means "head to head."