By 3 types, do you mean HA, SII and OIII? Or do you mean broadband, UHC, and emission line?
I don't tend to consider broadband and UHC filters as "narrowband", so I assume you're referring to emission line filters, which mainly come in the HA, SII and OIII passbands.
Also, I'm assuming you don't understand electron transitions or the EM spectrum (but these are fundamental concepts, so read up on those), so I'll leave the theory out of it.
In practical terms, you can only use narrowband filters on emission nebulae. This means that they will NOT work on galaxies, stars, star clusters, or reflection/absorption nebulae. Also, they need to be used with monochrome cameras (or contend with gross inefficiency).
The purpose of having 3 filters is to be able to generate a (false) colour image. Normal colour images are made up of 3 parts (here on referred to as 'channels'): a red channel, a green channel, and a blue channel. Normal colour cameras achieve this by using coloured filters on the pixels. However, since we are not using typical red, green and blue filters, we need to assign the images from the HA, SII and OIII filters into these colour channels to create a coloured image. The resulting colour image does not represent the actual colours of the object (at least in the way that the human eye would see if it were much more sensitive), but it is scientifically valuable for identifying the abundance of various elements. For astrophotography, this tends to create rather pleasing colour images.