Te-iru express the idea that something happened and that maintains the
state which was created by that event.
The door is open.
doa ga aiteimasu.ドアが しまっています。
A bottle of beer is in th fridge.
biiru ga reisooko ni haitte imasu.ビールが はいっています。
The shop is closed. Mise ga shimatteimasu.みせが あいています。
The verbs used in this expression are intransitive verbs.
Meanwhile, Te-aru express also the state but the difference from te-iru
is tre-aru sentence connotate someone did it with his intention