Instead of doing their job and coming up with a verdict, a jury in a trial currently being reported in the UK presented the judge with a list of questions to which they wanted answers. One question was "Can you define reasonable doubt?" The judge answered, according to this Guardian article, "A reasonable doubt is a doubt which is reasonable", which does not seem a terribly helpful explanation to me.
The jury has been criticised in several newspapers - for idiocy or obstinacy or lack of understanding of their role, depending on the stance of the newspaper - but I can understand why people might not be sure of the meaning of the phrase. The trouble is the word 'reasonable', which has a number of meanings. Presumably, 'beyond reasonable doubt' means 'there is no doubt' or 'we are virtually certain' (this phrase came up a week or so ago when archaeologists described the body found in Leicester as being 'beyond reasonable doubt' that of Richard III). However, if I say 'the price is reasonable', I just mean 'ok', and if I say 'my chances of passing the exam are reasonable' I mean 'quite good'. I would probably be allowed to use 'reasonable force' on an intruder, which means 'not too much'.
The OED's definition of 'reasonable doubt' is: "uncertainty as to the guilt of a criminal defendant; spec. doubt in the minds of the jurors that enough proof that the defendant is guilty has been presented in a criminal case".