Yes, it's very much related to the distribution of prime numbers. I've read a book by John Derbyshire called Prime Obsession that attempts to explain the what the Riemann Hypothesis is, its significance and relationship to the distribution of prime numbers, and historical developments in the attempt to prove or disprove the hypothesis. One particular devlopment was in 1896, when a conjecture similar to the Riemann hypothesis, but weaker, was proven, and the proof of that weaker conjecture was known to be sufficient to prove what is called the Prime Number Theorem.
Incidently, the subtitle of Derbyshire's book is perhaps in the process of becoming outdated (Bernhard Riemann and the Greatest Unsolved Problem in Mathematics). I recommend the book if you're really interested in knowing more about the Riemann Hypothesis. The book attempts to keep the mathematics at a level that can be understood by someone with high school education, but it does have to get into some concepts from calculus a little bit.
I might mention that not everyone has been of the belief that the Riemann Hypthosesis is necessarily true. Some actually have been of the belief it may be fairly likely to be false. For instance, it was long thought that Li(x)-pi(x) (where Li(x) means the logarithmic integral function and pi(x) means the prime counting function) is always positive. (Gauss apparently believed this to be "probably" true.) But in 1914, it was proven that this expression changes sign an infinite number of times (as x gets larger). But it appears that the first such sign change doesn't occur until x is well over 100 digits. So some think that just because the Riemann Hypothesis holds for such a huge number of cases does not necessarily suggest that it holds forever. It could be that if you just consider values of x so large where the prime counting function "doesn't behave as nicely any more" you may start to find counter-examples to the Riemann Hypothesis. (I've been paraphrasing information from Derbyshire's book here.)
