most favorite thing; absolute favorite
Emphatic phrase meaning something is one's very favorite; 大の acts as an intensifier similar to 'great' or 'big'.
The ramen at this shop is my absolute favorite.
She rereads her most favorite book over and over.
Combination of the intensifying prefix 大の (dai no, 'great/big') and お気に入り (okiniiri, 'favorite'). The exact historical derivation is uncertain, but it is a common emphatic expression in modern Japanese.