OK, this is how I understand the system.
Births, Marriages and Deaths are registered, and the brief details of these 'entries into a register' are recorded by quarters of a year in a separate register, a sort of index I suppose.
These entries are what are referred to: so 'birth registered Birmingham, 2nd quarter 1873, Vol 6d page 75.' means that in Volume 6d, on Page 75 are references to all births registered in the months of April May and June 1873. Birmingham district is not the whole city - just the district, others are 'Aston' and 'Kings Norton' which cover a larger area than the postal districts.
From the reference the register office can trace and issue a copy of the original certificate (sometimes direct copies, sometimes new certificates with the information transcribed from the original) if you want one.
Here is a picture of the entry for 2nd quarter 1873, part of the page. I've put red dots to show the reference.