to go into a place or thing: to enter, come in, pass in
This is a plain verb of motion meaning "to go in." It is built from the ordinary word for going or traveling (πορεύομαι) with the prefix "in-" attached, so it pictures someone making their way into a place: a house, a village, a city, the temple. Mark and Luke are especially fond of it, and most of its uses are simply people walking in through a door or a gate.
The same verb stretches naturally beyond people walking through doorways. It describes food "going into" the body in the teaching about what does and does not defile a person, and it reaches for things that cannot be seen at all: entering the kingdom of God, or worldly cares slipping in to choke a person's faith. In none of these is the meaning strained. English "enter" or "go in" stretches to cover the same range.
One fixed expression uses it in tandem with its opposite, "going out": to be "coming in and going out" among people is an old way of saying someone lives and moves openly and freely in their midst, carrying on public life without hiding. The two verbs together frame the whole of a person's daily comings and goings.