Overall there have been around 80 human studies that show that supplementing with probiotics can have positive effects by stimulating the resistence to infection.
The human gut contains different strains of bacteria, some of which are 'friendly' such as bifidum bacteria and Lactobacillus acidophilus, and some that are disease causing. Put simply, having lots of friendly bacteria in your digestive system helps to 'crowd out' the bad guys and stop them getting a foothold.
It is felt that Probiotic supplementation is more important to the older population as their levels reduce with age and this increases the chances of bad bacteria getting a hold.