Your rectum is the last bit of your bowel.
There are a few things that can happen in the rectum.
Having your rectum examined doesn't really hurt. To examine the walls of the rectum the doctor wears a glove and usually uses their index finger. They have some special jelly on their glove which they use to make their finger slip in easily. It's sometimes slightly uncomfortable but it doesn't hurt.
Bowel cancer is just one of the things that people are checked for when they have a rectal examination.
The whole point about having all these tests, examinations and operations is that, for example, with bowel cancers, very often if you catch them when they're only small you can cure them completely.
With regard to your dad...
The best thing is to tell your mum and dad that you would find it easier if they could tell you if there was something badly wrong.
(But think about this first to be sure you mean it.)
Lots of people find that, even though it's not nice to know, it's better to know that something bad is happening than to not know at all. Then they know exactly what they have to face and they can come to terms with it and work out a way of coping with it.
If that's how you feel then you should tell your parents and ask them if they can give you the information so you can know what's happening.