Colloidal silver is a mineral.  It is made of small silver particles suspended in a liquid. It is not made of a special types of silver particles but the same ones found in common items like dental fillings and jewelry. While it's typically found in liquid form, it has also forms that can be used topically and injected into the body. 
This solution was originally touted as a "cure-all" for various serious ailments and diseases ranging from herpes to HIV. It was and is still often marketed as a dietary supplement.
It was freely available over-the-counter in the United States until 1999. This is when the United States FDA claimed that it was not safe and was not shown to be an effective treatment for anything.
There is much debate about the supposed benefits of this solution. For one, it has not been studied very much and its "cure-all" claims have been called into serious question. Many medical professionals question its use as a supplement because the body has shown no need or benefit from additional silver.  The FDA and Federal Trade Commission currently crack down on health companies selling it as a dietary supplement due to the lack of testing and questionable safety, especially when it is used in homeopathy for serious ailments and diseases.
Some studies have found limited effectiveness shown with using this solution in topical applications in items like dressings and bandages for skin infections and wounds.  However, its other claims have been unfounded, which have resulted it being heavily regulated. Taking it, especially too much of it, may in fact be dangerous. One such issue that is common with taking too much is argyria, which is when too much silver builds up in body tissue causing it to permanently turn bluish-gray. Other reported issues from constant dosages of colloidal silver include headaches, upset stomach, kidney damage, poor interactions with several medications, neurological problems, etc.