It depends on the context, "snapping" could mean any of the following:
speaking sharply or angrily
breaking down emotionally
taking informal photographs.
It can also have its original meaning of breaking something, such as a stick or a rope, suddenly.
The joke is, presumably, a play on at least two of these meanings. For instance another character might say that they aren't breaking down emotionally these days and the person speaking would say that they weren't snapping as much meaning that they weren't speaking angrily on so many occasions, particularly to their partner.
I have now watched parts of the video and I see that the speaker is comparing the way in which she deals with patients and the way she interacts with her partner. The joke is that she believes that her own self treatment has reduced the extent to which she "snaps" at her partner and that this is a comparatively minor problem compared to those of her patients. Also her partner may not agree that she does not snap as much. Her revelation of part of her private life is a lightening of the serious mood of her talk.