They are actually miniature pressure sensing devices and radio
transmitters. They can sense (and report) a drop in the tire pressure
vs. a pre-programmed setting. They "talk" with a radio
transmitter-receiver in the car computer (somewhat similar to a
wireless Internet connection -WiFi or BlueTooth). The way they work is
as follows:

1) With tires pressure adjusted at the correct value, they get
"calibrated" by the car computer. Basically, the car computer send a
radio signal to the sensors mounted in the wheels to "learn" the
pressure and keep it as reference for future measurements. The
calibration is usually done by pressing a button on the car's dashboard
for 5 seconds or so.

2) Once calibrated, and with the ignition ON, the car computer "asks"
the tire pressure sensors to check the pressure and report back if it
is OK. The frequency with which the car computer communicates with the
sensors varies, but it can be as frequent as once every 5 seconds, or
as low as once every time the ignition is connected. The rest of the
time, the sensors are in a "stand by" mode consuming very low battery
power (same order of magnitude as a digital wrist watch). They only
become "alive" when activated by a digital radio code sent from the car
computer.

3) If the sensor detects that the pressure is signifcantly lower than
the normal value it was calibrated for, it will send a "Not OK" signal
back to the car computer, which will inform you via a warning light.

The technology combines developments from things like radio frequency
tags and wireless digital communication (Wifi, BlueTooth). The
interesting part is that because it only activates the sensors from
time to time, and the whole process takes miliseconds, the power
consumption is very low and the batteries in the sensors last very long
- typically as long as a set of tires, so the batteries have to be
replaced only when a new set of tires is installed.

Because specific sensors are designed to work with specific car
computer, I don't think they will work on trailer tires. Maybe if your
car is already equipped with low tire pressure alarm, your could try to
install the same type/brand of sensors which are installed in the car's
tires on the trailer. However, typically the car computer expects to
"talk" with four sensors at the same time, so hearing back from six may
confuse it (with upredictable results). Also, the transmission power
may not be enough to cover the distance from the trailer wheels to the
car computer.