Taking Steam for eg, it deals only with digital downloads, no retail. Now, when you buy a title via Steam, the title will get linked to your account forever (so to say). So, if you wanna play, you start up Steam and double click on the game in the library. That way, you don't require a disc to run the game. Also, with Steam you have the option of always keeping your games updated. If you opt for this, Steam will automatically update/ keep updated your games.
On retail, you'll most often need the disc to run the game. If a retail game requires an app like Steam, you won't need the disc. However, it is not necessary that retail versions will get updated automatically. You may need to update manually in certain cases.
Retail versions are cheaper than digital versions. For eg, Skyrim costs $60 on Steam. I got the retail for INR 1,200 = $20-$22 app. For that, I always prefer retail.
Steam again, on the other hand, has brilliant sales from time to time ranging from 20%-80% off the prices.
Retail: the discs have a lot of chances of getting scratched, damaged, etc, in which case, you'll need a fresh purchase. On digital, no such issues as there is no disc.
These are some of the differences between retail and digital.