Those little sections are mostly stand-alone pieces to be enjoyed just by themselves. Some of the scenes show small events that happen in the world of the main story, e.g. the cat walking on the street and after that Nano running past. Then later on we see Sasahara go home with Koujiro on the same streets. This is a bit of story telling and world building. Other sections like the rope skipping ones, are just little skits that use characters from the main story. Others like Helvetica Standard are completely disjoint from the main story. Later on you will see little skits and moments with characters never seen before and never to be seen again. Nichijou is a slice of life of which its title reveals it is a slice of life. A big theme is the appreciation of small moments otherwise unnoticed as we go through life. Sometimes that is just what it comes down to I think. Such as the peacefulness of a calm street or the beauty of the countryside. Nichijou also has some advanced language jokes where to western audiences the skit is nonsensical but to the Japanese audience an actual joke is presented. Other times it has a Koan type of vibe, where it is not meant to be understood logically. I really love all these little in between sections. They are unique and add so much extra depth and content to the show. I guess this is turning into just another ramble why Nichijou is so great so I’ll end it here lol.

My hypothesis is that Nichijou is a passion project and those are animation experiments to get your imagination working.

I don’t think there’s an explanation. Nichijou is, I think, based on a four-panel comic, not a serial, so there’s no overarching story, just a lot of vignettes. It’s silly and completely non sequitur.