Tag is the US name for a game children play where one child chases after other children.  The object of the game is for the child to touch  another child.  When he touches the other child he will yell, “Tag!”  

“Tag” jurisdiction is a way for a court in one state to consitutionally assert personal jurisdiction over an out-of-state defendant who visits the state where the court presides.  The court will have personal jurisdiction if the defendant is properly served while in the state.  “Properly served” means receiving proper notification of the lawsuit.  

For example, let’s say Peter sues Debby in New York.  Debby lives in Florida and New York does not have personal jurisdiction over her.  One day, Debby visits New York.  Peter serves notice on Debby of the lawsuit while she is visiting New York – –  let’s say he hands her a copy of the complaint and the court agrees that handing her the complaint is proper service.  Now the New York court can constitutionally assert jurisdiction over Debby, even if she has no other contact with the state.  This is similar to the game of tag children play because Peter successfully caught up to and “tagged” Debby

  Some videos on personal jurisdiction are here.