てある
te-aru
てある still has a person's fingerprints on it
The picture Something a person did deliberately and then stepped away from. Their intention is still sitting there.
Where the picture shows up in てある
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stuck up and left there
ドアに紙が貼ってあります。
doa ni kami ga hatte arimasu
There's a notice on the door.
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done ahead, ready and waiting
ホテルはもう予約してあります。
hoteru wa mō yoyaku shite arimasu
The hotel is already booked.
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chilled on purpose
冷蔵庫にビールが冷やしてある。
reizōko ni bīru ga hiyashite aru
There's beer chilling in the fridge.
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written down and still there
名前はここに書いてあります。
namae wa koko ni kaite arimasu
Your name is written here.
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left open on purpose
窓が開けてあります。
mado ga akete arimasu
The window has been left open.
窓が開いています just describes an open window; 窓が開けてあります says someone opened it and left it.