Poisson's ratio is a fundamental mechanical property of materials. When a material is stressed (i.e. stretched or compressed), it deforms in the direction of the applied stress. The ratio of stress and strain along the same direction (longitudinal strain) is a material property called the Young's modulus. However, an applied stress also causes strain in directions perpendicular to the direction of stress (transverse strain). Poisson's ratio is defined as the negative of the ratio of the transverse strain to the longitudinal strain. The negative sign is included because, as intuition suggests, tensile longitudinal strains correspond to compressive transverse strains, and vice versa.
Poisson's ratio is dimensionless, but if one insisted on including units then (m/m)/(m/m) would be most appropriate. Poisson's ratio is positive for practically all materials*. Most materials have Poisson's ratios between 0.2 and 0.5. Metals typically have Poisson's ratios around 0.3. Rubbers have Poisson's ratios near 0.5, which implies that volume is conserved. Cork has a Poisson's ratio close to 0. This property allows cork to be inserted into wine bottles without expanding laterally, inhibiting insertion or breaking the bottles.
* In 1987 polymer foams with negative Poisson's ratios were found. As far as I know these have no practical utility. See http://silver.neep.wisc.edu/~lakes/Poisson.html for more information.