What is a helping verb? If I was “taking swimming lessons” is the helping verb “taking” or “swimming”?

See below

A helping verb is a verb used along with another verb (forming a verb phrase) that helps add meaning and mood to the main verb. A helping verb is also known as a auxiliary verb. Here is a few examples: could, should, would, is, may, might.

In your question, the helping verb would be “taking”, as “swimming” is the main verb and is accompanied by “taking”, which helps add meaning to “swimming”.

Hope this helps!