The last integral is a surface integral. It is the fluid (current) flux crossing the volume surface integrated over the whole surface. It is how much charge is leaving the volume per second. ($\partial V$ means boundary of V.)

The last integral is a surface integral. It is the fluid (current) flux crossing the volume surface integrated over the whole surface. It is how much charge is leaving the volume per second. ($\partial V$ means boundary of V and you sum all local $j_\bot dS$.)