We've never been stopped by the police yet, but would have no problem explaining geocaching to them if we were.
We were however once stopped by private security guards and questioned. I made a formal complain about them, which I believe has resulted in a review of their procedures - because we were on public property not private property when they surrounded me in an attempt to make themselves look intimidating, and blocking off my passage past them. Because I had my littlest one with me, I didnt want any fuss, so answered their questions politely, and moved past them. They clearly were no wiser after I explained geocaching but didnt try to stop me passing them. I then studiously ignored them and carried on searching, while they hung about for another 20 minutes before getting bored and moving on.
My complaint centred around the fact these guys have absolutley no legal powers what so ever and have zero right or entitlement to question a member of the public in a public space. They effectively carried out what in law (here) is refered to as a stop and account. Only uniformed police offices can do this, or a PCSO in full uniform, or a plainclothes officer who shows you his ID. Noone else in law (here) can carry out a stop and account. There is also procedures set down as to the records they must keep and my access to such records. These security buffoons broke the law on several accounts and failed to keep any record. I also asked for a copy of the claimed cctv footage which Im entitled to, and was informed no cctv footage was recorded, despite cctv cameras everywhere. I further questioned why there was cctv cameras there if they werent recording, and why, if I was recorded in a public place, was the number for me to contact to view such cctv footage, not prominantly displayed, as is also required by law.
I have no problem what so ever with lawfully appointed police officers allaying their suspicions by questioning, but I despise these security buffoons who think they are a law onto themselves, most exspecially when they are questioning me, a member of the public, when they have no lawfull right to do so. I gather from reading logs in the area, numerous other geocachers have been harassed by these guys too. One even logged they won't be back to the area again because of these buffoons. I won't put up with it.