I too am new to running and just found the answer to your question a few days ago, so please correct me if I am wrong. Basically, qualifying times are used from previous races to either get into a more prestigious marathon later, or for marathons that are so large where qualifying times are used to get in line earlier than other slower runners so you don't have to run around them. For example, not just anyone can pay their money and run the Boston Marathon. You have to have ran a previous marathon with a "qualifying" time within your age group that is fast enough to get in. (I'm a 23 year old female, so I would need to run a marathon that was a "Boston Marathon Qualifier" and finish under 3 hours and 40 minutes to "qualify" for running the Boston Marathon later.) Also, the Disney Marathon is so large they use your previous qualifying times (from any previous race over 10K) to let you start in groups before they let slower runner start who eith do not have any qualifying times or who have qualifying times that are slower than yours.

Having run several Peachtree qualifiers myself I will chime in.  Keep in mind that although you need to run sub-55:00 to qualify for Time Groups 1A-B, if you submit a qualifying time that is longer than that you will be placed in TG 2-3 anyway.  With 55,000 runners and 9 TGs it is well worth submitting a time. (My qualifier last year was 61:13 and I got in TG 2)  Even if you're not sure you're going to run the Peachtree, it doesn't hurt to run a couple of qualifiers so you'll have a time to submit if you do decide to run it.  Also keep in mind that you can run the Peachtree without a qualifying time, but then you are randomly assigned to TGs 4-9.

What race are you running, BTW?  Is it in the Atlanta area?