The action requires focused attention on doing something with your hands. Some actions can occur in response to a Manipulate action, such as an enemy using Attack Of Opportunity to take advantage of you directing your focus away from them.
The Manipulate tag on a Spell or Metamagic means that the action(s) you use to cast the spell or apply the Metamagic requires either a verbal chant, a precise series of hand gestures or body movements, intense emotional focus, or some combination of the three. If the Spell or Technique does not have the Manipulate tag, and you apply a Metamagic to it that does, it gains the Manipulate tag.