I've mostly heard it in the context of building and construction videos where they are approaching a new skill or technique and have to remind themselves to slow down.
Going slowly and being careful leads to fewer mistakes, which will be a "smoother" process and ends up taking less time, whereas going too fast and making mistakes means work has to be redone and ultimately takes longer.
On rereading it, I see some parallels: When one is trying to go too fast, and is possibly becoming impatient with their progress, their mental queue fills up and processing suffers. If one accepts a slower pace, one's natural single-tasking capability will work better, and they will make better progress as a result.
And maybe its just my selection bias working hard to confirm that he actually is talking about what I want him to say!