Little bit of background
Everything in the world creates noise. Sometimes a little, sometimes a lot. In general, the hotter something is, the more noise it creates. This comes down to the fact that the hotter something is, the faster things move at the very lowest level.
In a resistor, there is a fairly linear amount of noise added to a system as the temperature goes up. The function of temperature to noise in a resistor is commonly used to identify the amount of noise added.
What's this actually mean?
In Antenna systems it is useful to be able to identify how much noise is introduced into a system. This is done with the Noise Temperature. A particular system will have a Noise Temperature associated with it. This is just saying that if your system were to be a perfect noiseless system, you could add a resistor in series at the temperature given and that is how much noise is being added.
Many times the temperature is way above what a resistor would ever be at, but it is just a very easy way to model and convey the noise in a system.
Going a little bit more in-depth
Thermal noise is generally modeled as white noise (noise that is equal at all frequencies) within what ever frequency range will make it through a system. In order to actually use noise temperature it is helpful to know the bandwidth that is being talked about. This is what the wiki page is calling the noise bandwidth.