ている Te Iru is a very common pattern, usually similar to English to English "be -ing", but sometimes indicating the state produced by an action.
てある Te Aru is a less common pattern indicating that a state has occurered because some preparation for it has been carried out:
電気が付けてあります。 Denki ga tsukete arimasu. 'The lights have been put/left on.'
電気が消してあります。 Denki ga keshite arimasu. 'The lights have been switched off/are off.'
ドアが開けてあります。 Doa ga akete arimasu. 'The door has been left open/are open.'
ドアが閉めてあります。 Doa ga shimete arimasu. 'The door has been closed/is closed.'
All of these verbs are usually (but not here) used with objects indicated by を o, e.g. 電気を付ける denki o tsukeru 'switch on the light'.