Packed To The Rafters Meaning

(idiomatic) Completely full; packed

Example: 2012 April 8, Holly Williams, “Mix and max: Designer Max Clendinning has had a radical change of heart when it comes to minimalism”[1], The Independent:
  The second reason his disliking of objects seems implausible is that I'm interviewing him in his Victorian terrace house in Islington – and it is packed to the rafters, often rather beautifully, with everything from Memphis glass to mid-century Aalto furniture to William Morris prints to Picasso plates...