@von-mises summed it up nicely enough, but you'll want to read the Wikipedia articles on heredity and hereitability, in particular the latter. Our genes can tell us so much about ourselves, but it's not always that simple. As you mention, there are lots of other factors that could and usually do come into play. Often times there isn't just one gene, but rather many genes playing a role (these are called polygenic traits). For example, see my answer to a question on hair color; there are dozens of simple changes that can affect the color of hair and eyes. These complex traits are really hard to tease out!
Additionally, not everything is 100% from genes; the environment can also play a huge role. Often we talk about how heritable a gene or a trait is by giving a percent, meaning how much of is due to genes you inherit from your parents. The heritability of IQ is an interesting read for an introduction to the concept.
So, what is the use of the genetic tests? Well, for starters, ancestry is really interesting and useful for people. Not just paternity or maternity (which is obviously accurate and widespread) but knowing where you are from. 23andMe is a great service (I'm 2.9% Neanderthal!) for finding out where you came from genetically.
There are, additionally, a number of traits that we've studied, or that do have strong genetic factors. Sickle-cell disease is a classic example of something just from your genotype, whereas other things are less determinate; for example, the heritability of baldness is around 81%, and I know from my genome that I have a slightly lower chance of becoming bald. There are other, more serious health risks that people would want to be tested for (BRCA for breast cancer, LRRK2 for Parkinson's, APOE for Alzheimer's) as well as inherited traits that are very genetically determined (like sickle-cell or Tay-Sachs).
In short, the genetic tests are very good at determining what the genotype is, which can be very useful for certain traits but completely useless for others. The more we learn about what our genes do the more we learn how complicated the whole system is. We are more than just our genes.