First I will start by explaining a small about on the differences that Single Layer and Dual Layer DVDs have.

Single Layer
A single layer DVD can hold a capacity of up to 4.7GB (the same as the size of a DVD-R). On a single layer DVD I would expect to find maybe a menu with access to a scene selection screen or just to play the movie. Due to such small size that single layer is compared to dual layer I wouldn’t expect to find any extras on the DVD.

Dual Layer
A dual layer DVD can hold a capacity twice the size of a single layer (hence calling it dual layer) which is 9.4GB. On a dual layer DVD I would expect to have special features and quite a few of them on as well. Also I would expect the quality of the menu to be far better. The only downfall to a dual layer DVD is that there is not and dual layer DVD writers out yet (and probably wont be) so due to this in order for us to make a backup of our film we may need to re-encode the film to make it down to approx 4.4GB so we can fit it on a DVD-R.

How To Tell What Layers You Have Got
Single Layer AKA DVD5 = Less Than 4.5GB
Dual Layer AKA DVD9 = More Than 4.5GB

How To Find Out
Double-click My Computer and then right-click on your DVD drive and select properties by left-clicking. If the disc is single layer the total capacity will be less than 4.5GB, if it's more than you have a dual layer disc.

Why do I need to know whether I have dual or single layer?
You need to know when you want to backup your film as dual layer is more complicated than single layer due to dual layer being more than what a DVD-R can hold you have to remove some extras and sometimes it is necessary to down-sample the film to fit on a DVD-R.