Interested in Language
I have read the expression 'on-the-go' to describe a feature of cosmetics (especially foundation makeups).
It originally means 'busy'or 'active' but do not understand what it means in cosmetics.
Not A Teacher
It is difficult to say what the meaning of "on the go" is in the context of cosmetics as the companies that sell them often use expressions in ways that are not normally used to describe the features of the makeup they sell.
It could mean that the cosmetic is hard wearing and will not smudge easily or that it is easy to apply for example, but without seeing the full context we cannot tell.