The word मीमांसा is derived from the धातु मान् (to know) + सन् and it means 'the desire for knowledge' and by extension 'discussion' and 'investigation'. It is used in these senses in the Veda itself.[TB p. 2]
It is called पूर्व 'prior' because it deals with the prior parts of the Veda as opposed to वेदान्त or उत्तर मीमांसा which deal with the concluding parts called the upanishads.
The object of investigation and discussion in पूर्व मीमांसा is धर्म.