"Wideband" is a radio set that uses more frequency range than it needs to.

An everyday example of what a wideband set is like this - If you are sitting at a restaraunt table eating amongst your friends with your elbows sticking out, you would be using more space than you need because you are intruding into other people's space. If you could somehow tuck your arms in you could do the same eating, but using much less space. This would be narrowband.

You and your friends sitting together from one end of the table to the other are the frequency spectrum.

Wideband and narrowband terms these days is directly related to how much data can be put through at once. Cpmplanies used wideband sets earlier on because of the lack of technology used in making the radio sets meant they had to space the frequencies out to prevent interference. Nowadays they can squeeze them together without interference.