The answer is: to escape.
The word elude can be used in many contexts, but in general it can be said to mean: to escape, get away, run away, from something, and usually by clever or ingenious means (he eluded danger).
It could also be used when someone fails to capture or grasp an idea or thought (the idea of justice eluded him). Also, finally, it could mean a failure on the side of someone attaining a certain goal or achievement (success eluded him).