I was scrolling on the Instagram and I found this random quote there: "swipe to get to know me". Why the "get" verb is on it? We just can say "swipe to know me" or not?
There is a difference between the process of learning to know somebody and the state of knowing them.
The verb 'to get to know' means the process of becoming familiar with somebody. Another way of saying it is to learn who they are or make friends with them. It's different from 'to know' because it assumes that you don't know the person yet. Knowing somebody is a state you reach after going through the process of getting to know them.
I would like to get to know you because you seem like an interesting person.
I don't already know you, but I would like to get to know you.
When you swipe on someone you don't know them yet and you won't know them immediately just by swiping. If they choose to respond then it means you have an opportunity to learn who they are, or 'get to know' them. This will take time and only after you've spent some time 'getting to know' them can you say that you know them.
Get has a number of meanings. One of the meanings of get is "to take" or "to obtain".
I think "to get to know me" has a rough translation to "to obtain (the opportunity) to know me"; but, because "get" has so many meanings, people could argue I've picked the wrong one.
For example, Andrew's explanation is a good one, and "get" could equally mean "become (knowledgeable of me) over time"