The prefix homo means same, so homozygous means that the organism has two alleles that are the same for a particular trait. The alleles could be both dominant (BB) or they could be both recessive (bb).
The prefix hetero means different, so heterozygous means that the organism has two alleles that are different for a particular trait. This means that the organism will have one dominant and one recessive allele (Bb) for the particular trait.
The term homozygous refers to an organism whose gene pair for a particular trait are the same. An example is a pea plant with two tall alleles (TT). The term heterozygous refers to an organism whose gene pair for a particular trait are different. For example, a pea plant with one tall and one short allele(Tt). In this case, the dominant allele of tall is seen in the offspring, however, it is carrying a hidden recessive short gene.