Genetics is the study of how traits, such as the colour and variety of your budgerigar, are passed from parents to their offspring. If we can understand how they are passed on we can breed for the particular body colours and varieties we like.
Traits are controlled by genes, which live in our cells so lets start there. We are all made up of cells, billions of them. Cells contain everything needed to keep us alive and well, but at the moment we are only interested is the part of the cell called the nucleus. This contains the genetic material that determines how we are made up. Inside the nucleus are the chromosomes.
Cells are constantly being made and dying. Part of the process of making a new cell is to copy the chromosomes from one cell to put in the new cell. All we need to know about chromosomes at the moment is that they carry the genes like beads strung along a string. Each pair of chromosome is made up of two identical copies of each chromosome (two identical strings of beads and therefore two copies of each bead).
Most of the cells in your budgerigars body have the two copies of each chromosome. However in the sex cells, the egg and sperm cells, there is only one copy of each gene. This is so when the sperm and the egg join to form the new being it has one copy of each gene from the egg and one from the sperm, giving it the required two copies of each gene.
On the right we have a pair of identical chromosomes. Lets imagine that the bars represent various genes, you can see how there are two of each gene, one on each chromosome. As we said earlier, genes control how we, and our birds, are made. So lets imagine we are looking at the gene that makes a budgerigar green, lets make it the thickest stripe below the middle pinched bit.
This is where this gene belongs; on this chromosome in this position. The place where a gene belongs is called its locus. Once upon a time this gene only produced a green bird. However one day a mistake was made when the gene was being copied for a new cell. So the gene produced a blue bird instead. Now the thing to understand is that it is the same gene, in the same locus, but it has been altered slightly. When you have different versions of the same gene they are called alleles.
So we have a gene with two alleles, the original one that makes a green bird, and the altered one that makes a blue bird. Your budgerigar gets one copy of this gene from its mother and one from its father, to make up the necessary two copies. If it receives two alleles that are the same it is said to be homozygous for that gene, if it gets two different alleles it is said to be heterozygous for that gene. Now this is really basic genetics, but it is enough to get us started with budgerigar genetics.