TMDSAS is the Texas Medical and Dental School Application Service. All Texas residents apply to the Texas schools through this service.
Secondary applications are applications that schools send you to request money and to fill out any additional information, maybe an essay of some sort.
TMDSAS is like AADSAS for the Texas schools (they have their own process). Some schools send out secondary applications in addition to the AADSAS main application with their own questions or requests for updated information.
Texas Medical and Dental School Application Service
Secondary apps are part of a dental school conspiracy to rob you of every last dime you have before you go into debt for the next 15 years of your life because the $1500 you spend on applications isn't quite enough for them. , but seriously, they are "extra" forms to fill out aside from the AADSAS that are used as supplemental material to aid in the schools decission process.
"I guess it shows the school is interested in you?" <--- RIIIGGGGGHHHHHTT
Most schools that require secondary fees don't necessarily require secondary apps in my opinion. All six of the schools I applied to required that I send them more money, but only one actually asked me to fill out a supplementary application with additional questions.