Most often a circuit breaker to cut or provide power to the room and/or to unlock the door. That’s generally fairly obvious, so if not, It’s possibly deprecated and bypassed. When being used as such it is typically just a power saving device. Imagine the annual cost saved, especially by large hotel chains.
While the other answers have elaborated on the primary reasons, I am going to point out what I perceive as a secondary reason and/or benefit:
The key has its fixed place.
To me as a hotel guest, this seems incredibly beneficial because it means the key does not lie around somewhere where I might forget it when leaving the room. Instead, it’s in its fixed place in the power slot, where I will invariably look before closing the room door. If the key is still there, I will notice it (and thereby spare myself of an embarrassing request at the reception desk to help a guest who was stupid enough to look himself out), and if it is not there, I know I have taken it.
Note that by disabling the lights when the key is not in the slot, the chance that I have put the key somewhere else upon arriving at the room the last time is close to zero.
Of course, this doesn’t work quite as nicely in a situation you describe:
though I’ve got the standard 2 cards for my room so I have another one anyways
Personally, I have stayed in hotels in various countries and never got two keys, unless I was there with my spouse, in which case each of use got one key and the method described above works again.
EDIT: This method works for any design of the “power card”, be it a credit card-sized key card, or rather the keyring pendant for a physical key, like this, or this, which may not easily fit into a wallet.
The 15 minutes problem is most likely caused by a faulty motion detector. Many hotels use a motion detector to switch off the main lights when the guest is sleeping. You can sometime notice this after waking up, sometimes the motion detector has not been triggered and then the lights don’t immediately work.
I have seen these cards control
Whether it exists and what it controls seems to vary around the world. In Europe it’s most likely to be lights, or lights and plugs. In the South Pacific it was usually just the airconditioner (and there was a sensor on the door to the balcony or deck that would also turn off the ac) or the ac and lights. In Europe the staff generally didn’t tell me what it was, in the South Pacific they generally did. I have seen these occasionally in North America.
It is easy to fool using either your second key, a card from your wallet you don’t need right now (grocery loyalty card say) or a folded up bit of card like a magazine subscription card. Some hotels don’t care if you do this, but in my experience, in hot places where it’s hooked to the ac they care. One place said there was a $50 fine if they found the ac on when you weren’t in the room. It is all about the cost of cooling and lighting a room you’re not in.
This feature is becoming increasingly common in many establishments. In my opinion the purpose of such card-activated time switches is to reduce costs: the removal of the card ensures that some/all electronic appliances are turned off when the guest leaves the room, thus saving money to the hotel. Indeed guests are often given one card to access the room which is also to be used in the slot you mention to turn on the lights and air conditioning. That same card they’ll have to take with them upon leaving the room, or else they won’t be able to get back in. Some card-switch makers claim a 40% reduction in electricity costs for hotels using their products.
It is worthy to note that some appliances are plugged in sockets that aren’t controlled by the card switch. This is often the case for the minibar/fridge, and sometimes for the air conditioning system too.
The case you mention of the lights turning off every 15 minutes is something I’ve never experienced, and sounds very much like if the switch was broken. Personally I would have contacted hotel management and asked for another room.
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