Hi Sheryl,
by entering the details of the DNA tests you have taken into WikiTree allows the system to calculate potential matches with other WikiTree users who have done the same. It also annotates all profiles that are biologically related to you with the percentage of DNA that you most likely share with them.
For example, if you look at the profile pages of your parents it will show that you should match at 50%. This, of course, is trivial in this case. It gets more complicated the more complicated the relationship.
On your profile page it shows that you should share roughly 0.78% with another WikiTree user. If you click through to their profile and then select the menu at the top of the page with their profile ID there should be a menu item called "Relationship To Me". Not the "Connection to Me" menu. Clicking on that will give you a page that says you are third cousins with this person, and that your common ancestors are Rebecca E (Ernest) Switzer and Winfield Scott Switzer.
Going to Rebecca's profile, and choosing the menu with her profile ID should give you a "DNA" menu item. Clicking that will give you a tree of who she inherits from, and access through the tabs at the top to other details - such as which profiles descend from her .
These are predictions, though, the complexities of DNA mean that you may not match exactly 0.78% with that other user. You are both tested at 23andMe - so if you don't find him in your matches there it means that the DNA you inherited from your common ancestors is different from the DNA that he inherited. According to this page at 23andMe there is only a 90% change of detecting a third cousin.
According to DNA Painter third cousins should share between 0 and 234 cM of DNA, with an average of 73 cM.
So, in brief, the DNA functionality on WikiTree doesn't find matches, it predicts who you should match, given ideal circumstances.