A genotype is a combination of all the gene variations (aka Alleles) your cells contain, mostly regarding the genes contained within the nucleus of an eukariotic cell.
All eukariotic cells have their nucleic genes contained in a number of chromosomes, i.e. a supramolecular cluster containing DNA and proteins. Chromosomes of a non-reproductive cell always have a 'twin', that's why they say that a normal human cell has 2n chromosomes - n usual chromosomes and as many twins. Chromosomes that are twins of each other are called homological.
Homological chromosomes contain the same array of genes in the same order. But just as twins may look similar yet act differently, so do genes within homological chromosomes may yield different variations of a trait. If two slighly different genes are 'twins' of each other, i.e. they are located at the same spot of two homological chromosomes, they are called alleles. E.g. if peas are yellow, they are thought to contain one allele. If the allele is different, you MAY be getting green peas. If we try to denote this on paper, it may look like this: A - allele allowing yellow peas, a - allele allowing green peas.
So: two 'twin' chromosomes have the same gene which may have variations called alleles. There're two possible variants to go from here: either both chromosomes have the same allele (AA or aa), in which case we have a homozygous genotype, or one allele may be different from the other, in which case we have a heterozygous genotype (Aa).
The properties yielded by given genotypes depend on the type of dominancy: if one allele is fully dominant in relevance to the other (full dominancy), then you simply have to look for the dominant allele. E.g. AA and Aa both have A which is dominant, and since A gives us yellow peas, AA and Aa are genotypes of yellow peas. In aa no dominant allele is found, therefore the peas are green.
If dominancy is not full, then the whole thing is even easier! Each genotype variation has its own property outcome (aka phenotype). E.g. A - allele allowing red flowers, a - allele allowing white flowers, then AA - red flowers, aa - white flowers and Aa - pink flowers.
Sometimes chromosomes are also denoted, which may look like this: X(H)X(h) or I(A)I(B), where X(H) is an X chromosome with allele H, I(A) is the first chromosome with allele A and so on. Heterozygous genotypes are those containing various alleles: I(A)I(B) is heterozygous, I(A)I(A) is not.
All given examples are from monohybrid cross, when you study the heredity of a single trait. If we study two traits, say the color of peas and their 'wrinkledness', then we'll have dihybrid cross, and 'wrinkledness' will have their own allele pair located on a different chromosome pair and therefore inherited independently. If we say B is for smooth peas and b is for wrinkled, then AAbb means yellow wrinkled peas, and aaBB - green smooth peas. As you can see, both pairs in each example are homogenous, so each example is called dihomozygous. Diheterozygous genotype looks like this: AaBb. In case of full dominancy it means yellow smooth peas.
