AKA a hair receiver.
In the Victorian era a hair-tidy was an item commonly found in a middle- to upper-class lady's toiletry set. It was most often some sort of decorated jar with a lid that had a wide opening, although baskets were also used. It was used for holding any hair that came out when combing; this hair was collected and then used to make 'false hair', AKA 'rats'. These were rolls of hair sewn into fine hairnets, used to fill out fancy hairdos.
A few pictures: 1., 2., 3.