As covered in the grammar point for ところ, this noun is used to specify the exact moment 'just before' a verb's action takes place (when the verb is in its non-past form). When だった is added, however, it changes the meaning to emphasize that the event that was 'about to' occur did not actually happen in the end (often because another event took its place). This can be translated as 'almost (did something)' or 'was on the brink of (doing something)'.

• あっ、危(あぶ)ない！財布(さいふ)を忘(わす)れるところだった。
  Whoa, that was close! I almost forgot my wallet.
• 間違(まちが)った電車(でんしゃ)に乗(の)るところだったが、駅員(えきいん)さんが教(おし)えてくれた。
  I was just about to get on the wrong train, but a station attendant pointed it out to me.

The verb that is used with ところ may also be combined with the auxiliary verb ない. In such cases, it conveys that a particular outcome was 'almost not' achieved, but was successfully accomplished at the last moment.

• あれは最後(さいご)の一個(いっこ)だった。もう少(すこ)しで買(か)えないところだった。
  That was the last one. I almost wasn't able to buy it.
• 電話(でんわ)したとき、予約(よやく)でいっぱいで席(せき)が取(と)れないところだった。
  When I called, it was so fully booked I almost couldn't get a table.