A mammoth is a prehistoric creature much like an elephant, but with bigger tusks. The word is also used to describe something really big. It's significant in Van Halen lore because that was their original band name.
When Wolfgang Van Halen, son of the guitar god Eddie Van Halen, started working on his first solo project in 2015, he called it "Mammoth WVH" in tribute. This song ties into that theme, but the word "mammoth" shows up just once in the lyric:You've found the way
A mammoth weight
right off our shoulders
In a Songfacts interview with Wolfgang Van Halen
, he explained: "'Mammoth' was one of the first ideas written for the project in mind. The demo title was 'Mammoth 1.' So, I cheekily squeezed the word 'mammoth' into the bridge so I felt comfortable enough calling the song 'Mammoth.'"