This is probably one of the less surprising rules. When you were at school and the principal walked into assembly, you all stood up until they told you to sit down. If you're in court and the judge enters, everybody rises, and the judge will tell then when it's acceptable to sit back down again. It therefore makes sense that when the Queen of England is standing in your presence, you better get up on your toes sharpish!
Standing before those with greater social status than you has been hardwired into us since we were born, and you see examples of it everywhere. The military is a good example; no Private would dream of sitting on their haunches when a Sergeant entered the room. The good news is that the Queen probably won't leave you on your feet for an extended period of time. She's getting on in years now and would much prefer to be sitting down herself.