Sometimes days go speeding past
I know every words of this phase, just don't know the meaning of this combination.
This is kind of a bit of personification. You can imagine a car "speeding past" you if it drives very quickly past you on the street.
The language here applies this idea to a day instead of a physical object. It just means that the day seems to go quickly.
On the other hand, a day could 'crawl along', meaning time goes very slowly.