It might be a UK thing? They're actual physical donation bins that are often located in public (council-owned) car parks and supermarket car parks (as well as at the council-run recycling centre). A lot of them only take clothes and shoes, but some of them take household linens as well.

Most of them are run by charities, who sell the good quality donations in their shops. Anything that's not suitable for the shops is sold to textile recyclers who shred it so it can be used to make things like the padding in car seats.

Here's a nice photo of what the donation bins typically look like: http://www.charitybags.org.uk/images/wikimedia-org-clothes-recycling-containers-rushmere-craigavon-co-armagh-ni.jpg

I'm very lucky in that I have easy access to both clothing/textile and book recycling bins (the book recycling bins are fairly similar in appearance).