Ruskie,
Hi - I'm attaching a non-graphical JPG representation of what you get in your list of DNA related cousins from 23andMe, and I suspect FTDNA's is comparable (I think DevonCruwys has some other screenshots on her site, linked above in this thread).
People set up a profile where they can put in details of their family surnames, dates, and geographic areas. If you find an individual that seems to have a high degree of relatedness you can do a preliminary look for matching surnames and geo-locations before making contact. As a wild (but real) example, if you find someone who has 23% of the same DNA as you, and look at the profile and it says, "I was adopted at birth and have absolutely no idea of my family tree", you know you have just found a half-sibling, or a sibling of one of your biological parents.
A more reasonable expectation is to find someone who shares under 1% of your DNA, but that is still relevant in a genealogical framework. Most people put emphasis on those who share 0.34% or greater as a start.
Let's look at some of my stronger matches. The 0.73% match at top is quite possibly a descendant of one of my Dad's many, many second cousins (less likely on my mother's side because of relative number of 2nd cousins they each had. We haven't made contact yet and he has little detail in his profile.
The 55 cM, 2 segments means there is a fairly long length of matching DNA at either 2 places on one chromosome, or one place on each of two chromosomes. The DNA doesn't lie and we are definitely related. The I1a1 is his paternal haplogroup that is very close to mine (I1), and the string starting "R1" is his maternal haplogroup (mine is H6a1).
I have just made contact with a person who shares 0.25% of my DNA with a significant 19 cM stretch on a single chromosome. He is on a business trip, so we haven't been able to compare genealogies, but three of his names match my own, and they were in the same area of Pennsylvania in the same timeframe as one of my 3x great grandmother's family. I have made a tentative conclusion that his relative might be a sibling or aunt/uncle, but will wait until we can compare details. If I am right and he has a good genealogy, I might be able to determine which one of the 3 possible couples are the actual parents of my 3x ggma.
Hope this helps,
Nick