What does the fittest mean in an evolutionary sense?

Animals are the best adapted to an environment and can flourish.

'Survival of the fittest' has never really made sense, because it confuses the scientific (evolution, 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.