I’ve heard this expression a few weeks ago, when I went to apply for my visa. The process involves quite a bit of waiting, which can be quite tiring for kids (well, parents too). There was an American family with three children and all of them were quietly reading or watching cartoons on their iPads, so when the parents were told that they were free to go for a walk and come back in an hour or so, they decided to stay put so as not to disturb the children.
The meaning is not hard to guess – to remain in the same position.
Here are some examples:
– Stay put. I’ll be back in a minute (MacMillan Dictionary).
– If you go for a new job you will face the stress of a new role (which may impact on your ability to conceive), having to wait to start a family, and potential hostility at your new role if you become pregnant as soon as you start trying. I think you should stay put. This way, you can start a family straight away (The Guardian).
– Then, earlier this afternoon, an order came down from a Moscow city court to clear the camp. The protestors were split: some suggested relocating to the Old Arbat, a famous Moscow street; others wanted to gather in front of a statue to Karl Marx; and a third faction proposed staying put and waiting for the riot police. (The Economist).
– Most employees plan to stay put, reveals Deloitte global survey (hrmagazine.co.uk)