This is what NDVI values measure. Many research projects (some are listed below) have shown that is can be an indication of vegetation health, density, and biomass. This measure is mainly driven by precipitation. This is why you may hear some people describe areas of an image as "wetter" or "drier" instead of "more green" or "less green."

Sources:

Avery, T.E. and G.L. Berlin. 1992. Fundamentals of Remote Sensing and Airphoto Interpretation. 5^th ed. Upper Saddle River, Prentice-Hall, Inc.

Boone, R. B., K. A. Galvin, et al. 2000. Generalizing El Nino effects upon Maasai livestock using hierarchical clusters of vegetation patterns. Photogrammetric Engineering & Remote Sensing 66(6): 737-744.

Chen, D. and W. Brutsaert. 1998. Satellite-sensed distribution and spatial patterns of vegetation parameters over a tallgrass prairie. Journal of the Atmospheric Sciences 55(7): 1225-1238.

Diallo, O., A. Diouf, et al. 1991. AVHRR monitoring of savanna primary production in Senegal, West Africa: 1987-1988. International Journal of Remote Sensing 12(6): 1259-1279.

Li, Z. and M. Kafatos. 2000. Interannual variability of vegetation in the United States and its relation to El Nino/Southern Oscillation. Remote Sensing of Environment 71(3): 239-247.

Oesterheld, M., C. M. DiBella, et al. 1998. Relation between NOAA-AVHRR satellite data and stocking rate of rangelands. Ecological Applications 8(1): 207-212.

Paruelo, J. M., H. E. Epstein, et al. 1997. ANPP estimates from NDVI for the Central Grassland Region of the United States. Ecology 78(3): 953-958.

Peters, A. J., M. D. Eve, et al. 1997. Analysis of desert plant community growth patterns with high temporal resolution satellite spectra. Journal of Applied Ecology 34: 418-432.

Ricotta, C., G. Avena, et al. 1999. Mapping and monitoring net primary productivity with AVHRR NDVI time-series: statistical equivalence of cumulative vegetation indices. ISPRS Journal of Photogrammetry and Remote Sensing 54(5): 325-331.

Schmidt, H. and A. Karnieli. 2000. Remote sensing of the seasonal variability of vegetation in a semi-arid environment. Journal of Arid Environments 45(1): 43-60.