During this phase any ships that you have instructed to move will jump to their destination sector if their operational rating permits such travel.  A ship's engine rating determines the maximum number of sectors (hexes) that a ship can move in one turn.  Ships jump straight to the destination sector without traversing the intervening sectors, so no scan information is generated for those intervening sectors.  There is no stacking limit to sectors; any number of ships from any number of empires can occupy a given sector.

A ship damaged in combat may not have sufficient operational engines to move to the specified destination, in which case the damaged ship will not move at all, so be careful when planning movement for a ship under attack.  A ship cannot move and fire in the same turn. 
 
You can specify movement orders for individual ships or for groups of ships in the same sector.  Individual movement orders are useful in a combat zone when you want to move each ship to a different destination.  Group movement is useful when you want to move some group of the ships in the same sector to the same destination.  If a ship is damaged before moving, it's possible that it will not possess enough operational engines to reach the designated group destination.  In this case, the damaged ship will be dropped automatically from the group and will not move; the remainder of the group will move normally.
 
Abandoned Empires:  Abandoned ships which are present at foreign worlds (and which are not ordered to self-destruct or fire) will move along the shortest routes (including wormnets) toward the nearest friendly or allied world (choosing the world with the highest friendly-DP-to-foreign-guns ratio in case of a tie).  Abandoned ships between worlds will hold their positions for the first turn of abandonment, but will move on subsequent turns toward the nearest friendly world.  An abandoned ship with a scan rating of three or more will be deemed a scout/scanner, and will always hold its position between worlds.