As you can see from the video, 'get on' and 'getting on' are popular and versatile phrasal verbs in both a social and professional context. While they have a variety of different uses, the theme of progress or progressing with something is quite common.
For example, if somebody asks you how you are 'getting on' with a task, they want to know how you are progressing with it. Similarly, if somebody asks you how you are 'getting on' with someone, they want to know how your relationship or friendship with that person is progressing. If you 'get on' in life, or in a task, you likewise make progress with it.
This theme even stretches to cover time. If somebody was to look at their watch and remark that it is 'getting on,' then they are saying that time has progressed to an advanced stage of the day, or, more simply, that it is late. If a person is said to be 'getting on in years,' then that means they have progressed to an advanced stage of their life, or are old.
Another common usage is to refer to boarding something, particularly a form of transport like a bus, train, plane etc., or to joining something, like a team.