>To be filled beyond regular capacity
> To be filled up to the brim
The phrase refers to the ‘seams; (the place where one piece of cloth is stitched with another one) of clothing that threatens to rupture when the garment that is made out if it is too tight for the individual wearing it. It is used in a hyperbolic manner.
>Why did you have to invite everyone to this small party? Our house is bursting at the seams and looks like it’s about to get trashed, too!
>That was a wonderful meal, but I’m bursting at the seams.