It's no secret that a huge part of the Queen's job is to meet various different people from all over the world, and in many circumstances it involves meeting lots of people in a short time period.
Her Majesty always puts on a kind and polite display, but if she spent too long conversing with everyone she met, she'd simply never get anything done - which is why she has become a master at ending conversations as politely and briskly as possible.
During her 70 years on the throne, the Queen has become an expert at this, with many people who have had the pleasure of meeting her commenting on she got them to step back after shaking their hand.