V-て（transitive）+ ある
has been done (and left that way)
Something was done deliberately by someone and the result remains. The doer is not mentioned — the point is the present state. Contrast 〜ている with an intransitive verb: 窓が開いている is "the window is open"; 窓が開けてある is "the window has been opened (by someone, on purpose)".
壁に地図が貼ってあります。
かべに ちずが はって あります。
A map has been put up on the wall.
切符はもう買ってあります。
きっぷは もう かって あります。
The tickets have already been bought.