Difference between dominant and recessive genes
Strictly speaking, there is no such a thing as a dominant or recessive gene. A gene is a section of the DNA that encodes a particular instruction, or a set of overlapping instructions: a basic unit of inheritance. A single gene can encode a single trait (though in most cases the mechanism is more complicated), for example the color of the pea plant flower, or a human blood group. Different versions of the actual trait exist: some peas have red flowers, some have white flowers. These traits are determined by different versions of a single gene. These gene versions are called alleles.
Some biologists talk about dominant and recessive alleles, but technically speaking, only traits (in our example, the red or white flowers) can be recessive or dominant.
What does "dominant" and "recessive" mean?
A diploid organism (such as a human being, pretty much any other mammal or, for that matter, a pea plant) has two copies of most genes: one is inherited from the mother and the other one is inherited from the father. For simple traits encoded by a single gene (like the pea flower color), this means that each plant has two alleles of the flower color gene. Let's call the allele that encodes red flowers R and the allele that encodes white flowers W. Each plant would thus have one of the three combinations: RW, RR or WW. The plants that carry RR combination will have red flowers, the plants that carry WW combination will have white flowers. The plants that carry a RW combination, however, will not have pink flowers: their flowers will be red. We can thus say that the red flower color is a *dominant trait*, or more precisely, that red flower color is dominant over white.
Geneticists have a conventional way of writing out dominant and recessive traits. The dominant trait is written as a capital letter and the recessive trait as a lower case letter. So for the pea flower color, red is R but white (or lack of red) is r, not W. This is just the most common convention (there are others). The possible combinations listed above will be thus conventionally written out as Rr, RR (both produce red flowers) and rr (produce white flowers).
Many genes have more than two alleles. The gene for the main human blood group exists in three alleles: A, B and O. Of these, A and B blood groups are dominant over O, but co-dominant against each other. Thus, a person with an AA genotype will have an A blood group, but so will a person with a AO genotype. A person with a BB genotype will have a B blood group, but so will a person with a BO genotype. A AB genotype will result in a AB blood group, and only a OO genotype will produce a O blood group.
A fertilized egg cell is called a zygote and from the point of view of each gene, the organism can be a homozygote (with two identical alleles, eg AA, BB or OO in case of the blood groups) or a heterozygote, with two different alleles (AB, AO or BO).
We talk of complete dominance when (short of DNA analysis) a heterozygote is impossible to tell apart from a homozygote with two dominant alleles. This is the case with human blood groups A and B: it's not possible to distinguish between a person with a AO genotype and a person with AA genotype, they both have the same blood group A.
Many traits conferred by dominant alleles are not completely dominant. If T denotes dominant, tall stem and t denotes recessive, short stem, an incomplete dominance will mean that homozygote TT will produce tall plants, a homozygote tt will produce short plants, but a heterozygote Tt, although producing taller plants than a homozygote tt, will still produce shorter plants than a TT heterozygote.
In human beings, several body characteristics are dominant over others.
Brown eyes are dominant over other eye colors (though eye color inheritance is not a simple process). Detached ear lobes are dominant over attached ear lobes. Ability to roll the tongue into a tube is dominant over lack of such ability, phenyloketonuria to lack of it, hemophilia to normal blood clotting, dark hair over blonde hair, blonde hair over red hair, normal color vision over red-green color blindness.
The dominance mechanism explains how two parents lacking a particular trait can have a child that exhibits same trait: for example two parents with an A blood group can have a child with a O blood group if both of them have actually a AO genotype. For the same reason, two brown eyed parents can have a blue eyed child, and two brown haired parents can have a blond (or even a red haired) child.