Why do devices continually look for a network?

When I look at the network under the WiFi symbol I find that my computer is continually looking/checking for networks. Is that normal?

Yes. But it happens much more frequently when you are actually checking with the wifi open.

It is standard part of wifi operation.

I would just like my computers/Kindles/iPads to hang on to my network and stop looking for others.

Mostly there are no controls.. or they are buried deeply into the configuration files and not accessible to run of mill humans.

If you turn it off.. then it cannot work in another room where you have a different router. It will be stuck forever (without intervention) on the one AP.

Due to wireless interference and the overall saturation of the 2.4ghz band in particular.. without some sort of auto scanning the wireless won't work.

You should be able to improve the situation by using 5ghz only (that doesn't work on kindle but is less relevant since you download the book).

Make sure you have high signal in the room where you use the device.. and as little interference as possible.

LaPastenague has already provided you with an excellent reply, but I would like to add a bit of info about the networking "magic" that occurs in background with wireless networks to, hopefully, answer the reason "why" your devices are constantly searching.

Basically, your wireless router sends out a beacon signal every few milliseconds so that wireless devices looking to connect can find it. Once a device "sees" this beacon, it then exchanges a series of communications with the router to actually establish a connection. After the connection is make, the client will periodically "confirm" that connection by sending another series of communications and this is when you would see the "searching" messages.