I got this question the other day. Sometimes I forget others don't know hair talk. If my client asked, I'm sure others have the same question.
Highlights are lighter or brighter strands of color. This can mean going only one shade lighter or 10 shades lighter than the base color. The process can involve foils or it can be painted. The painted-on process is also known as a balayage. One misconception is that if someone is getting highlights then the end result will be blonde. That is false. Brunettes can definitely get highlights and remain brunette. Getting highlights will add dimension to the base color.
Lowlights are when you add strands of a darker shade to the base color. If the client has highlights, this can simply be a lighter shade than the highlight. Adding lowlights can increase the dimension of one's hair or add richness to the base color.
Adding highlights or lowlights can change someone's look dramatically. It can also be a subtle change.