The idea is that exposure to antibiotics, processed foods or synthetic foods disrupts the balance of internal flora in your gut. The bacteria native to your body are involved in all kinds of processes that your body needs to survive. Probiotic supplements are created upon the premise of dysbiosis... either there are not enough beneficial bacteria in the body or their populations are unbalanced, leading to disease. I think there is truth to this, but the marketing hypes it up way too much.
One thing that most people don't know about probiotics is that if you are not buying ones that go in the fridge, then they are useless. Probiotics on the store shelf are lifeless. The genuine article always requires cold storage to keep the bacteria alive. The other thing is that most pill-form probiotics are not enteric coated, which means many of the probiotic bacteria you ingest are killed in the stomach acid. The only way to affect maximum intestinal exposure is to get an enteric coated variety so that the pill passes through the acidic environment and only opens up in the basic environment of the small intestine.