|Everyone is related. The term "related" or "relationship" is used
within the context of a "recent" relationship -- i.e. within approximately the
last 1,000 years. This is the period of interest to most genealogists.
Research before that time is made more difficult due to the lack of family
surnames and the absence of records.
DNA evidence is a series of numbers. If two people have matching
numbers, they may be related. The more numbers that match, the more likely
they are to be related. (These numbers are called "markers" or "alleles".
A marker is the position on the DNA chromosome where the change took place, and
the allele is the count of the number of molecules at that position.)
DNA changes very slowly and randomly, but the change is passed on to the descendants of the person who experienced it. The odds of a marker changing again or returning to a previous value is unlikely, making it a unique identifier of a family branch.
A "haploGROUP" is a designation given to a large group of people descended from one common, ancient ancestor. This type of mutation is called a "SNP" (pronounced snip) and each of them is believed to have occurred only once in human history. People possessing the same group of SNPs are descendants of the same branch of the human family tree. In other words, they belong to the same haplogroup. (See Wikipedia's definition of haplogroup and McDonald's world haplogroup frequency map.
The haplogroup is the genetic genealogist's starting point, but something is needed to differentiate more recent branches of the family, something which changes more often than the SNP. This faster-moving (faster mutating) part of the chromosome is the STR (Single Tandem Repeat). The STR signature of a haploGROUP is the signature of the ancient ancestor who experienced it. The test results for each participant in the DNA Project are their own unique DNA signature. That person's signature is called a "haploTYPE". Variations of the haplotypes from the ancient haplogroup signature identify more recent branches of that ancient ancestor's descendants.
DNA isn't used alone. Accurate pedigree information of the participants allows us to combine it
with the DNA data to come up with useful DNA signatures and to then identify and
isolate the spurious mutations which occurred more recently and which might
otherwise confuse the analysis.