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In biology, fitness is the number of offspring of a particular organism which survive to reproductive age. In other words, fitness may be thought of as the ability of an organism to pass on its genes. The usage of "fit" in this context, refers to the adaptation of an organism to its surroundings.
Misconceptions of fitness
Evolution is often summarized (read as: oversimplified) as "Survival of the Fittest." In more expanded terms, this means that evolution favors mutations or adaptations which increase the fitness of their host organism. For the most part, that makes sense to people, but here's where the misconceptions start to leak in: to be fit, an organism does not necessarily have to be the strongest or survive the longest. An extreme example would be the following: suppose Organism A has a gene which makes it reproduce five times more viable offspring but makes it die at a very young age. Organism B, on the other hand, has a competing allele which makes the organism survive five times longer but produce far fewer viable offspring. Which one is more fit? The answer, as long as we keep things simple, is A. It may not live as long, but it produces way more copies of its gene, which in turn produce way more copies until Organism B is just a tiny minority.
Another related misconception about fitness is that it can be termed simply in number of offspring. This is right only as long as we consider viable offspring. An organism that has a thousand offspring but ignores them after birth may not be as fit as one which has only a handful but invests a lot of energy in them (e.g. humans).
Things which affect calculating fitness
Note here that we're not talking about the actual factors which may increase or decrease fitness. Rather, the focus here is on factors which may affect our evaluation of a gene in terms of fitness. These can come in a variety of forms, but the salient point is that looking only at the number of offspring produced is often overly simplistic. One must also look at the health of each of these offspring and their reproductive success.
The term "heterozygote advantage" applies to a gene which imparts some sort of advantage when present in only one copy (that is, when the organism is heterozygous). The most common example involves the gene for sickle-cell anemia. When a person is homozygous-dominant for this trait, their red blood cells are normal; when they are homozygous-recessive, they are prone to sickle-cell anemia. However, sickle-cell heterozygous humans have increased immunity to malaria. So, it's adaptive, but not in double doses.
In terms of individual selection, this concept does not have many implications, but the ramifications of heterozygote advantage in terms of gene selection can be fairly complex. A gene "wishes" to create copies of itself, not copies of its competing allele. However, in the case of heterozygote advantage it is actually beneficial for the gene to cooperate with its competitor, contrary to what simple gene-selection theory might predict.
Selfish Gene Theory and fitness
Some of the problems of thinking of fitness can be solved if we break away from the idea of an individual and start thinking from the point of view of the gene, as first suggested by Prof. Dr. Richard Dawkins in The Selfish Gene. The gene "wants" only to produce more copies of itself, and so it could be considered successful if it contributes to the creation of a body which passes on more copies of that gene. It could go about this a variety of ways, from the creation of a number of low-quality bodies or the creation of a few high-quality bodies. The quality doesn't matter; what matters is how many copies of the gene the new body can pass on. That's fitness.
- Richard Dawkins; The Selfish Gene; Oxford University Press; Oxford, England; 1976