Visualize a space so filled there's no room left, illustrating an extreme degree of fullness. My bookshelf is stuffed to the gills; I can't fit another book!
Pro Tip 2/3
Not Literal
'To the gills' doesn't mean something is literally filled with fish parts; it's just an expression. His suitcase was packed to the gills, barely closing.
Pro Tip 3/3
Negative Expression
Often used to describe uncomfortable situations due to excessive fullness. We left the concert early because it was packed to the gills.