Let give an example of an experiment where you want to perform an analysis with an excitation at 295 nm. If you set a bandwidth at 5 nm, it means that the slits will excite at 295 plus or minus 2.5 nm i.e. from 292.5 to 297.5nm. The slitwidth will represent the physical opening of the slits, mainly in millimeters, necessary for the fluorimeter to achieve its 5nm bandwidth.

The bandwidth is an absolute value when the slitwidth will depend on the architecture of each apparatus. You will do exactly the same with the emission.

Apart the fact that these values are essential to reproduce the experiment, they are essential to perform a correct design of an experiment.

Let take another example: you perform a FRET experiment between two fluorophores, let say Alexa Fluor 532 and 568. Even if you are not familiar with FRET experiment, try to visualize the two excitation and emission spectra (I suggest you the excellent Spectra Viewer of Invitrogen) and I will give a simple explanation.

You excite the donor at 532 nm: it will emit a fluorescence with a max at 570 nm able to excite the Alexa 568. You record then the fluorescence at 600 nm that is the maximum of emission of this fluorophore.

If you have a 5nm bandwidth, you will record from 597.5 to 602.5 nm : you can see on the spectra that you will record also 30% of the fluorescence of the Alexa 532 donor fluorescence.

I you have a 10nm bandwidth, you will record from 595 to 605 nm : you can see on the spectra that you will then record more than 60% of the fluorescence of the Alexa 532 donor fluorescence.

Your results will be considerably corrupted.

The slit and bandwidths are the gaps of excitation and emission windows of luminescence spectrophotometer, which gives us idea of how much quanta of radiations have been used for excitation and then emitted back.

The slit and bandwidth are two coupled parameters of  any spectral devices: than  slit  is less the less is bandwidth  which determines  spectral resolution of  devices. It means that You can change  the spectral resolution  in some  interval  depending on  spectral bandwidth  of absorption (fluorescence) bands  of a sample You deals with in order to record true spectra. 

Not sure how important the two parameters are for your tests but in general the slit width and the bandwith are very important.

They both refer to the monochromator settings (note there are two monochromators: excitation and emission one) and there is an input and output slit on each of them. The bandwidth is related to the slit size. In general, the bigger the slit the higher the bandwidth value (and lower resolution of your spectra). The bandwidth for the given slit size depends on the dispertion of your grating inside the monochromator.

Hoe it helps :-)