Does a dominant trait mean it is the most common trait? Why or why not?

Yes dominant does mean the most common trait, but I think it would be better to say "more common" than most because there are only 2 types of traits, dominant and recessive. The dominant trait is more common because it appears more often in a population and dominates a recessive trait when appearing next to it.

Allow me to explain it regarding alleles.

When you have one trait, there are 2 types of alleles involved, the capital letter (dominant) and the lowercase letter (recessive). In this case, let's say our trait is height and we'll use the letter H as our allele character.

There are three types of traits you can create with alleles.

HH (which is purebreed dominant) Hh (which is heterozygous dominant) hh (which is purebreed recessive).

Notice how with the Hh, the trait is still dominant. This is because dominant alleles always hide the recessive alleles when paired with them. This causes a higher percentage of dominant-led traits and is the reason why they are so much more common and are the "most common" of the two total traits involved.