A quantitative and analytical investigation on the conduction mechanism in p-type cuprous oxide (Cu$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$O) thin films is performed based on analysis of the relative dominance of trap-limited and grain-boundary-limited conduction. It is found that carrier transport in as-deposited Cu$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$O is governed by grain-boundary-limited conduction (GLC), while after high-temperature annealing, GLC becomes insignificant and trap-limited conduction (TLC) dominates. This suggests that the very low Hall mobility of as-deposited Cu$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$O is due to significant GLC, and the Hall mobility enhancement by high-temperature annealing is determined by TLC. Evaluation of the grain size and the energy barrier height at the grain boundary shows an increase in the grain size and a considerable decrease in the energy barrier height after high-temperature annealing, which is considered to be the cause of the significant reduction in the GLC effect. Additionally, the density of copper vacancies was extracted; this quantitatively shows that an increase in annealing temperature leads to a reduction in copper vacancies.