A period of increasing growth before the log phase in a culture of microbes.
After the culture is started on a medium, at first there is no growth (the lag phase), and then the microbes start to gradually grow (acceleration phase) until they reach a constant maximum rate of growth (log phase).
From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.