To get on is to board a bus, a train or a plane. Also, in British English, to have a good relationship with somebody.
The boarding sense is the plain one and is the opposite of get off. The relationship sense is extremely common in Britain and takes with, so getting on well with a colleague is a standard phrase. There are two more: getting on with a job means continuing, and getting on in years is a gentle way of saying somebody is ageing. Getting on for a number means approaching it.