What exactly is a centimorgan?
I personally like to talk in Morgan (M), instead of centiMorgan (cM), because the Morgan has a more intuitive meaning than one-hundredth of its value.

Morgan

If two loci are at distance 1M, it means the expected number of cross-over happening between these two loci is 1. If they are at 0.1M, then the expected number of crossover is 0.1. If they are at 1.4M, then the expected number of crossover is 1.4.

centiMorgan

As the typical distance of interest is much lower than the Morgan, we typically talk in centiMorgan.

Rate of recombination

If in a given meiosis, there is 0 crossover between two loci, then the two alleles from the same haplotype will end up in the same gamete. If there is 1 crossover, then the two alleles from the same haplotype end up in different gametes. If there are 2 crossovers between two loci, then the two alleles from the same haplotype will end up in the same gamete.

In short, if the number of crossovers between two loci (which expected value is the number of Morgans) is even, then the two alleles from the same haplotype will end up in the same gamete.

At very low Morgan (say 0.000001M), the probability of having an odd number of crossovers is low and the recombination rate is therefore low. As the number of Morgans increases, this probability of having an even number of crossover approaches 0.5. The recombination rate can therefore never be greater than 0.5.

Physical distance

Note that as the recombination rate per nucleotide varies throughout the genome (and among genders and among lineages), the distance in Morgan between two loci is not a simple function of their physical distance in number of nucleotides. The two are obviously correlated though.

Human genome

In the human genome, the average per nucleotide recombination rate is of the order $5\cdot 10^{-8}$ (Wang et al. 2012). This means that 1 cM is about 1.5 millions of nucleotides.

Highly Related posts

This question has actually been answered several times already. You'll find more information, some drawings and some math at the posts


Recombination frequencies
Genetic linkage greater than 50 centimorgans


For a more introductory post, have a look at 


Why do we need two markers to measure a recombination rate?