When stating 'I was about to' you are informing someone that you were going to do something, but another event prevented you from doing it. It is similar to 'I am about to' but the difference is that you will not do it any longer. Since you will not do it any longer, it becomes a past event. That is why we use 'was' instead of 'am'
Here is an example conversation to help you understand.
A: Hi Mike. I need to ask you a favor. B: Hey Bob. what do you need? A: Can you drive me to the convenient store? My car is in the shop and we really need to get milk. B: Sure. I can do that. A: Were you in the middle of something? I don't want to bother you. B: I was about to watch a movie, but that can wait.
In this case, he cannot say, "I am about to watch a movie" because he will not be watching it because he has to drive his friend. You use "I was about to" when you will not be doing something immediately because of some other event.