Tournament size affects the way individuals are selected for breeding the new population. When creating a new population, the process is as follows:
1. Select [Tournament Size] individuals from the old population.
2. Take the fittest of these and make a copy of it.
3. Mutate the copy, cross its genes with another individual's or leave it be.
4. Place this copy into the new population.
5. Repeat 1-4 until the new population is filled.
So as you can intuit, increasing the tournament size decreases variability in the new population but decreases the mean fitness. For example, if you set the tournament size to the size of the whole population, you'll only get mutated copies of the single best individual. If you set it to 1, the selection of individuals for the new population is entirely random and has no fitness component. There is a trade-off between the desired selective power of fitness and the variation that you wish to maintain in the population to keep it from stagnating.