〜てある
has been done (and is still so)
Thing が + transitive verb て-form + ある
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て-form + ある describes a state that someone created on purpose: 窓が開けてあります, "the window has been left open" (someone opened it, for a reason).
It uses verbs that take an object (開ける, 書く, 貼る), and the thing becomes the subject with が.
Compare ている with the matching verb that has no object: 窓が開いています just says the window is open, no one in the picture. 窓が開けてあります implies a person did it deliberately.
It's what you use to describe what's been set up or written: 本に名前が書いてあります, "the book has a name written in it"; 壁に地図が貼ってある, "there's a map up on the wall".
Examples
換気のために、窓が開けてあります。
The window's been left open to air the room.
壁に地図が貼ってあります。
There's a map up on the wall.
テーブルに花が飾ってあります。
Flowers have been set out on the table.
ビールはもう冷やしてありますよ。
The beer's already been chilled.
この本に名前が書いてあります。
This book has a name written in it.