An Elf-Hat is a hat made especially for a House-Elf.
History
In the 1995–1996 school year Hermione Granger continued the Society for the Promotion of Elfish Welfare-group (SPEW), that she started the preceding year, and made some Elf-Hats and disguised it as rubbish, in the hope that a House-Elf would pick it up, and be freed automatically. Most House-Elves refused to clean Gryffindor Tower, in fear of accidentally picking up clothing, leaving Dobby to clean Gryffindor Tower by himself. Dobby took the hats when cleaning the Gryffindor common room and tried to balance them on his head.