The website for Klaire Labs has a link to an excellent and very informative article about probiotics. To download it in PDF format, go to this page (which has some good basic information on it)- on the bottom to the far right side you will see a link for "Making Sense of Probiotics". It gives extensive information for the different species of probiotic microflora and what they do, including discussions of which strains can help with specific health conditions.
Here is one quote that I found especially enlightening about the role probiotic play in immunity:
"The intestines are the primary immune organ in the body. The bowel-associated immune system contains the largest mass of lymphoid tissue in the human body, a vitally important component of total host immunolgic capacity. Bowel mucosa and lymphoid tissue are closely linked immunologically with gastrointestinal microflora. Substantial evidence associates probiotic bacteria with modulation of host-mediated immune responses. Probiotic bacteria boost both innate and acquired immune responses. These include increases in circulating lymphocytes, stimulation of phagocytosis and antigen-specific antibody secretion, and increased production of interferon-gamma and other cytokines."