When I was in an elementary school PTO, the Volunteer Coordinator was one of our most important positions. In our group, key goals included for us to provide a channel of communication and to coordinate most volunteer activities within the school.
We sent a detailed volunteer sheet home to parents at the beginng with a list PTO activities, school events, and classroom activities (including volunteering for room parent) and parents checked off which ones were of interest. (Note - when we changed the form to include two columns for Adult1 and Adult2, we really started getting some response from the dads as well.)
Anyway, that went into a big spreadsheet that we could sort by teacher, grade, volunteer name, student name, interest area.
When we had an event, the volunteer coordinator organized the volunteers - sending out notes, making calls, monitoring sign up lists. While one person did most of this, she could draw on others as needed, depending on how big the event.
We gave each teacher a list of volunteers for their classroom, including who was willing to to be class parent (and those were worked out by the teacher.)
Also under this umbrella, we instituted "Grade Parents", to enhance communication back and forth between PTO and classes. So it was sort of like a tree
PTO
** Volunteer Coordinator (1)
** Grade Parent (K-5, so 6 ppl - generally also a room parent)
** Room/Class Parents (about 30)
When a grade had something coming up, like certain testing phases where they needed extra monitors, the teachers or grade parents would let the PTO know and the Volunteer Coordinator would work with the Grade and Class parents to recruit the help. Grade parents were also part of of our (large) board and each made a breif report at each board/business meeting.
Somethings, like field trips, didn't really need our help as there were always so many parents of children attending willing to sign up with the teachers.
But we facilitated volunteers wherever we could, and the Volunteer Coordinator headed that effort.