It means "come to be in", possibly "find oneself in".
In other words, it is used to indicate the arrival of the subject into
a new state of some kind, differing from a previous state. So it
has to do with beginning or starting, in a way.
'get into trouble' - come to be (in the state of being) in trouble
'get into a dialog/conversation' - come to be in the state of having a dialog/conversation - start a conversation
'get into a habit' - come to be in a (certain) habit (of doing something)
CJ