While I'm not an expert in inorganic semiconductors, it means that either the concentration of charge carriers or their mobility increases with the application of a magnetic field (in organic semiconductors the increase of charge carrier population is known as field-doping). That said, you might want to have a read of the following papers:
In non-magnetic materials, a negative magnetoresistance can be due to an additional Hall-effect which in turn is due to a transverse current, which in turn is due to surface recombination.
Negative MR at low temperatures is usually a consequence of disorder-induced localization. For 2D weakly-localized systems, it should be possible to describe your MR data using the Hikami-Larkin-Nagaoka model; the temperature dependence of the resistivity may also exhibit a logarithmic divergence at low temperature. For a strongly-localized (i.e. highly disordered) material, R(T) will follow a variable-range hopping law and the negative MR can be much larger (assuming that Coulomb repulsion hasn't opened a gap at the Fermi energy).
I thoroughly recommend reading Efros and Shklovskii's (excellent) book to obtain a deeper understanding of your data.