Why add breadcrumbs to meatballs?
In meatballs or meat loaf or even burgers, breadcrumbs are sometimes added with egg. 

The bread, if unseasoned, doesn't change the flavor much except to dilute it. 

The texture is definitely different. It is smoother and spongier. The breadcrumbs also soak up liquid so the product doesn't lose as much and stays moister.

Purists often decry the use of breadcrumbs in things like burger patties. For myself- I will add breadcrumbs when I am in the mood for the breadier texture- often when I will be adding extra liquid flavorings like Worcestershire or liquid smoke and want to strengthen the structure a bit.