To talk about an action that was in progress or a state that continued for some time in the past, Japanese uses ていた (or the polite form ていました). This structure is formed by combining the て form of a verb with いた, the past tense of the ichidan verb いる (to be).

• エアコンがついていたので、部屋(へや)は涼(すず)しかったです。
  The room was cool because the air conditioner was on. (Was in the state of being on)
• 私(わたし)が電話(でんわ)したとき、彼(かれ)はテレビを見(み)ていた。
  When I called, he was watching TV. (Was in the middle of watching)
• 子供(こども)のころ、東京(とうきょう)に住(す)んでいました。
  I was living in Tokyo when I was a child.
• 家(いえ)に帰(かえ)ったら、ドアが開(あ)いていました。
  When I got home, the door was open. (Was in the state of being open)

In some situations, ていた is used for an action that may still be happening. The speaker uses the past tense to describe what they observed previously, often to politely make a suggestion or because they aren't certain if the situation has changed. This is much like the English phrase '(A) was doing (B)'.

• お姉(ねえ)さんがパソコンを使(つか)っていたから、後(あと)で宿題(しゅくだい)をするよ。
  My sister was using the computer, so I'll do my homework later.

In this sentence, the action of 'using' is not necessarily over. We can infer that the speaker is saying 'my sister was using the computer when I last checked, and she probably still is, so I can't use it now'.

This same sentence structure would also work if the speaker had left the room where their sister was, and as a result, does not know for sure if she is still using the computer.