It’s the code of the county and hospital where the mother gave birth:
The first 2 digits (23) identify the county code= county Miami-Dade
second 2 digits (10) identify the facility number, with numbers from 00-88 referencing a “specified facility” such as Clinic, Center, health care center, hospital)
http://hsc.usf.edu/NR/rdonlyres/840A327E-97B7-47F8-82DD-A01F...

Based on the above directory, “23-10” refers to the "Anne Bates Leach Eye Hospital" (a somewhat unlikely facility to give birth in :-)

However, based on this site, 23-10 is the code for the “Edgewater hospital”:
http://katsprogis.tripod.com/id7.html

And yet another site claims that 10 refers to “Jackson Memorial hospital”
http://www.city-data.com/forum/miami/2592832-anyone-born-hia...