Barbara, 

this question is about the lesson section pasted below. The point is that ‘lessons’ can be implicit here in French. 

At least in my part of the English speaking world, there can be a similar distinction in English between ‘ goes dancing ‘ and ‘ does dancing ‘ - the former suggesting more a repeated unstructured undertaking for pleasure, while the latter suggests a more structured and focussed situation, seeking improvement.

ATTENTION:

When using "faire de la danse" or "faire de la natation" (FOR EXAMPLE) rather than simply "danser" or "nager", you refer more to an organised, repeated activity - I take dance lessons / I go swimming [as a regular activity, e.g. attending class or lessons] - than just a 'one-off' activity you're in the middle of doing such as I'm dancing / I'm swimming.