Elephantiasis is a devastating condition, characterized by enormous swelling of the extremities (usually the legs). It is caused by a worm called Wuchereria Bancrofti (among other similar worms), which is transmitted from infected individuals to uninfected individuals via the bite of a mosquito. The worm then spreads to the lymphatic system, a system of vessels like arteries and veins which carry extra fluid from the tissues back into the heart. The presence of the worm blocks lymphatic drainage back to the heart, leading to massive fluid build-up in the affected extremities.
Even in regions of the world where elephantiasis is present, it is very, very rare, and contact with an affected person is not a method for spreading the disease. In addition, simply being bitten by an infected mosquito is not sufficient for developing the disease, which likely requires infection by the worm as well as individual susceptibility (a problem with the immune system) to develop.
Elephantiasis is a treatable condition with medications, particularly in the early stages; later-stage infection with very large swelling of the legs can require surgical repair which is not always completely successful. Although you should be reassured that you most likely did not contract elephantiasis from the individual you saw, it is not possible to make any diagnosis over the internet; if you have concerns, you should contact your primary care doctor
for an evaluation.