Homozygous and Heterozygoas can be referred to as words that are used to indicate the nature of alleles of a certain gene.
Since we know that alleles of a gene are present in specific locus of the chromosome. as organisms contain two copies of each chromosome, therefore, the allele of genes are also true. These gene encode for specific traits like height, complexion, eyes shape etc.
Now what homozygous means is that the gene of any trait has two alleles that are exactly similar to each other and both encode same variety of a trait. For example, Suppose Black eye color is denoted by gene B while blue is denoted b and allele for black eye is dominant over allele for blue eye.
Now if the organism is homozygous for black eyes, it means his genotype is BB, while if the organism is homozygous for blue eyes, it means its genotype is bb.
Now what heterozygous means is that the gene of any trait has two alleles that are different to each other although both are for same trait. If we take example of eye color, any organism that has black eye color but his genotype is Bb will be heterozygous. Phenotypically he will have black eye but actually he also posses allele for blue eye and he will transfer this allele to his offspring and there are chances some of his kids to have blue eyes.
Hope it helps!