What does "fit" mean in "survival of the fittest"?
'Survival of the fittest' has never really made sense, because it confuses the scientific (evo. biological) and colloquial definitions of the word - which some of the previous posters have also done.
Biological fitness simply refers to an individuals genetic contribution to the following generation. That is, a 'fitter' individual, in an evolutionary sense, is one whose genetic material is proportionally overrepresented in the next generation.
The mechanism by which an individual achieves this may include out-surviving competitors, but it's certainly not the only way to increase fitness. Two individuals may live for the same length of time, but one may successfully court more females, or out-compete the other for food resources, for example. So when we refer to a 'fitter' individual (or individuals), we're saying nothing about why they are so. It's not a comment on their 'fitness' in the human sense of the word (bigger, stronger, longer-living), it simply refers to how well they pass on their genetic material.
So you can see why the phrase is nonsense. If we're being precise, then 'survival of the fittest' translates to 'survival of the individual who is better able to pass on their genetic material to the next generation' - which is meaningless because it tangles up these different concepts.
Rather than "fitter", I'd say "better". Better at hunting, gathering food, surviving predators, surviving weather conditions or other kinds of population pressures. The better a population gets at the above things, the more (and fitter/better) offspring it is likely to have and the pyramid goes on.
In some cases, mutations might simply confer a "new" advantage that there was no prior pressure in the system for. For example, I can easily imagine a bird population where one of them evolves a plumage/pigment mutation that gives it a selection advantage and it quickly becomes the norm. This mutation could have - theoretically, and in my view - evolved even in the ABSENCE of a sexual selection pressure.
It's just that natural selection (in my simplistic interpretation) "favors" any improvements in organisms in a really simple, statistical way.
Often it is re-phrased "Survival of the Most Adapted." Fittest might make you think of the strongest or the fastest, but suppose in extreme famine, those who had better regulation of muscle growth could have more surviving generations. In an over abundance of resources the reverse could be true.
Ultimately in natural selection, it's all about getting your genetic information to as many surviving copies or permutations as you can. Many organisms use DNA to hold the information, but there are other options (RNA viruses for example).
Getting back to the phrase: It's saying that the fittest is the one who continually replicates well in the current environment/surroundings. Ecosystems are often changing, thus who has the best fitness will change as the ecosystems changes. When an ecosystem is stable for a long period of time, you will find highly adapted organisms to that ecosystem. This is because the selection towards "fittest" has been applied to many, many generations.
While, as others point out, "survival of the fittest" is a pithy description of the theory rather than an actual serious statement I think it can be converted to a useful definition relatively easily.
There is substantial debate about how, exactly, fitness should be defined. I'm not enough of an expert to want to try and lay out the complications here but I will give my preferred definition:
The fitness of an organism is defined as the number of its grandchildren that make it to adulthood (or that number divided by two for sexual organisms).
This has the advantage of being amenable to experimental investigation and intuitively simple while complex enough to avoid simple problems arising from the differences in offspring number and the question of infertile offspring.
It might sound tautological, but fitness is pretty much defined as 'being more likely to survive - and reproduce'; fitness is surviving and survival goes to the fittest.
This is a trite way of citing Richard Dawkins' theory of the replicator to describe fitness.
Fitness is a property of being able to carry one's genes to a later generation. Fitness is result of the individual properties and how well the individual can get along in the environment that it finds itself, in comparison to other individuals who might be competing for resources in that environment.
There is no concrete definition of fitness. Fitness can mean size and strength, or lightness and resilience, short or long life. There is no a priori way of looking at two individuals you know nothing about and deciding which is going to be more successful at reproducing.
not sure this is better, but there's definitely more of it...