to go over from one place or condition to another: to depart, move on, or pass across
At heart this is a simple word for going across: leaving one place and turning up in another. In the Gospels it is mostly Jesus on the move, departing one region and arriving at the next (Matthew 12:9; Matthew 15:29), or an instruction to relocate, whether that is a missionary told not to shuttle from house to house (Luke 10:7) or a mountain commanded to shift from here to there (Matthew 17:20).
The same verb also carries the weight of a bigger crossing. John uses it for the believer who "has passed from death to life" (John 5:24; 1 John 3:14): the ordinary moving word now names a change of state, a transfer from one condition into another, and the wording treats it as already accomplished. In between sits Jesus' own departure "out of this world to the Father" (John 13:1), where a plain leaving quietly stands for his death.
The two poles are one idea seen at two depths, which is why they belong to a single meaning rather than two: crossing over from where you are to somewhere else, whether that somewhere is a town down the road or a wholly new standing before God. It is close in force to μεταίρω for moving on, and its Hebrew counterpart is עָבַר, the verb for crossing over that likewise reaches from a literal ford to a change of state.