Blinking is when elves let light pass through them and they disappear. Vanishers do it naturally as they move, but other elves can do it with practice and for a few seconds.
In Book 1: Keeper of the Lost Cities, Fitz proves to Sophie that he is an elf by blinking, which makes her freak out.
In Book 2: Exile, Sophie ends up blinking while flying, which Keefe called the Amazing Flying Foster Routine. It is later discovered this is due to her teleporting ability, and not because she was blinking.
In Flashback, Della and Biana are pictured to blink out of sight for longer periods than normal at Alvar's tribunal. This indicates that Vanishers blink out of sight for longer periods when they are in particularly negative moods.