During this phase you can reset the transponders for your ships so that they conceal themselves from foreign empires.   Once a ship is concealed, only foreign ships in the same sector will be able to identify it (i.e., those that have it on SRS).  Foreign ships in nearby sectors will only see the ship as "unidentified tonnage."  You can, of course, only conceal ships that you own.
 

Allies: Allied empires can never conceal ships from one another.
 

Abandoned Empires: Abandoned ships will always be concealed from non-allied empires.