What is a 'crab', and how does one perform/obtain one?

The person was referring to crab walking (or doing the Spycrab), which is a set of movements you may perform that are amusing in the 3rd person perspective (but not as much in 1st person).

To perform the Spycrab, equip your Disguise Kit, crouch, and look upward. Walking around will make you look like a crab.

More recently, as an acknowledgement of this community phenomenon, the Disguise Kit was given a second taunt that performs a Spycrab, which may have been what the person was talking about. This taunt is performed at a reduced chance (empirically, it appears to be about 20-25%).

The random nature of this taunt has lead to the creation of a gambling game often played on trade servers, where participants pay some amount of metal, then repeatedly taunt with the Disguise Kit until they Spycrab. The last remaining player who has not Spycrabbed wins the pot.