Okay, so now you have a good broad understanding of what they are, the question remains should you actively consume them? I have studied this subject extensively, and yet I claim no definitive expertise on it because there is so much ongoing study. However, here is what I can tell you.
As far as I have come to understand after review of multiple sources, probiotics do no harm. Of course, that statement only holds true within reasonable limits. If outlandish quantities were consumed (trillions), I'm not sure what would happen. For example, even drinking too much water can be harmful as it would overwhelm the kidneys and flood the gastrointestinal system.
So if it probiotics aren't harmful, does that make them helpful? For general use, the jury is still out, but the overwhelming consensus and numerous previous studies suggest that they provide no real benefit for a person with a healthy gut. Changing the bacteria composition of one's gut is not easy under normal circumstances, and in fact, most commercially available probiotic products neither contain sufficient colonies (need at least 1 billion) nor the wide range of different types of good bacteria to make any difference.
(As a side note, carnivores (meat eaters) typically have different bacteria colonies than herbivores (plant eaters). The significance of this fact is not well understood at this time. Also, immediate family members often have the same bacterial colonies and if a family member wants to be restored to their historical composition after a bout of serious infection or illness, it can be accomplished by fecal implant through a nasogastric tube or sometimes through a fecal enema.)
So when are probiotics helpful? They are helpful when you are taking a course of antibiotics, which by definition kills all bacteria, good and bad. The probiotics help to replenish the healthy bacteria even as the unhealthy perish. Probiotics are also believed, based on several studies, to be helpful with diarrhea, dysentery, and allergic gastritis. In fact, with diarrhea related illness, they are said to reduce symptoms and duration of disease by as much as 50%.
(On a personal note, I can attest to their apparent efficacy after recently being afflicted with such a viral illness. Taking probiotics gave me some relief, even if it was only through peace of mind that I was doing something to help myself. Imodium and electrolyte replacement with pedialyte helped as well.)
Some studies report benefits from taking probiotics with Irritable Bowel Syndrome (IBS) and inflammatory bowel diseases such as Crohn's Disease (Terminal Ileitis) and Ulcerative Colitis. They are also reported to be useful for atopic eczema (a skin condition most commonly seen in infants) and with Helicobacter Pylori or H Pylori as it is often referred, infections, now known as the main cause of gastric ulcers.
The good news is that studies are continuing and we expect to have more definitive answers in the not too distant futures.
In the interim, I suggest you save your money and only use probiotics when either something has already gone wrong that may be amenable to correction with probiotics, or in the case of you are taking antibiotics where they may prove protective.
Notwithstanding, make sure that you only use products that contain at least 1 billion colonies and have at least a few different strains. VSL3, Bio-K, and Lactobacillus GG seem to be three reputable products. (No, I have no financial or other relationship whatsoever with any of these manufacturers.)
The best advice I can give you is be careful what you put in your mouth, don't eat anything if you are not sure it is fresh, and wash your hands well before eating. Also, learn how to manage your stress. These protective measures may spare you ever needing a probiotic. Stay healthy, my friends!