What you have said above is absolutely correct. I feel that you have a better understanding of this than you might think...
So, a punnett square is a useful tool in looking at the heritability of a single trait or two traits; there is a more advanced method for looking at three or more traits. When you set up a punnet square with one trait, this is called a monohybrid cross (mono meaning a single trait).
You will have to open in new tab by copy and pasting link.
This picture is probably similar to what your teacher showed you. So the letters of the top represent one parent and the letters to the left represent the other parent. The reason each parent has two letters is because they received two alleles (version of gene); one from each parent. The spaces with the flowers in them represent the offspring and each offspring also receives two alleles of the gene; one from each parent. In this case B (purple) is dominant to white, which means, in order for there to be a white flower, it must have two small b's (bb).
This can be very confusing at first, but once you start doing them, it makes much more sense. Please let me know if you have any other question. I'd be happy to help.