I carry two climbing ropes in my gear, as I might need to suspend myself between two trees for access to a place where one rope might not suffice. But this is an extremely rare situation. I can only remember one time when I used both ropes.
What you're probably referring to is Doubled Rope Technique (DDRT) vs. Single Rope Technique (SRT). In each case you're climbing on one rope, but in DDRT it's doubled over a limb (or similar tie-in point) above you, and you're connected to both ends of the rope. In SRT, the rope is locked off and you connect and climb on one end of it.
DDRT is more of a basic method and less gear intensive. Most of us agree that this is where you begin. SRT requires more gear--ascenders--and more cost, but some guys love it. The difference between the two is basically technique and personal preference.
Start from scratch. Get good instruction from someone experienced & qualified to teach, and you'll understand in no time. Then you can decide which is best for you.