It is defined as "A vector that denotes the magnitude and direction of lattice distortion associated with a dislocation." (Callister, Materials Science and Engineering an Introduction, 776)

The Burgers vector can be used to identify the nature of a dislocation in a crystalline structure. If the Burgers vector is parallel to the dislocation line, this indicates a screw dislocation. If, however, it is perpendicular, this indicates an edge dislocation. An angle other than these (other than 0, 90, 180, 270 degrees) is indicative of a mixed dislocation.

For a given dislocation line, which may change direction and nature in one crystalline lattice, the Burgers vector will remain the same. In metallic materials, the direction will be in a close-packed crystallographic direction, with magnitude equivalent to the interatomic spacing.

In face centered cubic and base centered cubic structures, the Burgers vector may be expressed as

b=(a/2)[hkl]

where a is the unit cell edge length and [hkl] is the crystallographic direction having the greatest linear atomic density. As some basic vector math will tell you, the magnitude of the vector is

|b|=(a/2)(h2+k2+l2)1/2

And the direction is, of course, (b/|b|).

This information was derived from my Materials Science and Engineering lecture notes.