At its core, biological evolution deals with how the frequencies of different alleles (gene variants) in a population change over time. Even though mutations are occurring all the time, these mutations do not constitute evolution unless they are able to become prevalent in a population. There are two main ways by which such mutations could spread throughout a population: natural selection or genetic drift. Under natural selection, mutations that confer selective advantage spread throughout the population because individual that carry these mutant alleles have more offspring than those who lack the allele. Under genetic drift, the mutation confers no advantage, but it becomes prevalent in a population through random chance.
For both of these processes, the rate at which mutant alleles to become fixed in a population (i.e. for these alleles to outcompete all other versions of the gene), depends on the size of the population. Even alleles that provide strong fitness advantages will be fixed at slow rates in very large populations. Therefore, the large size of the human population (and the ease of mixing, so that no subpopulations can get isolated from the larger population) will make any significant changes to the human genome occur at an extremely slow rate. That is not to say that evolution has stopped; indeed, there are numerous examples of alleles that have become fixed rather recently in various populations throughout the world (for example, alleles for lactase persistence which allow individuals to digest milk sugars into adulthood, mutations in the CCR5 receptor which are thought to provide resistance to the plague and smallpox, and mutations in genes that affect alcohol metabolism. See
http://www.nytimes.com/2010/07/20/science/20adapt.html for additional discussion).
Under what conditions might we expect human evolution to occur more quickly (relatively speaking since evolution occurs on geological time scales)? See the following post for a more in depth discussion:
https://www.physicsforums.com/showthread.php?p=4511126#post4511126. Note that new technologies may allow for artificial selection in human populations and could greatly speed human evolution in the near future.