A system interlock was a function of the transporter used to synchronize the pattern buffers of one or more transporter devices. The system interlock was essential to proper and safe transit between two connected transporter systems.
In 2364, Natasha Yar attempted to interlock the USS Enterprise-D's transporter beam with that of the Sanction to facilitate beam-out. (TNG: "Symbiosis")
Engaging the interlock could cause ionic fluctuations to occur within the matter stream during transport. This was the case in 2369 when Reginald Barclay beamed back to the USS Enterprise-D from the USS Yosemite in the midst of a plasma streamer. Because of this, Barclay was able to see the quasi-energy microbes (actually members of Yosemite's crew) that were trapped within the matter stream. (TNG: "Realm Of Fear")
When Sargon made it possible for the away team to beam through solid rock, it is likely a form of interlock was used between the Enterprise and Sargon's transporter systems.
The first time that two transporter pads are seen used in tandem like this occurs in "The Trouble with Tribbles" when crew members are seen dematerializing from the Enterprise transporter room and rematerializing on K-7's transporter pad. It is implied that some kind of interlock of the two systems is being used, as is often the case when transporting from one Federation location to another, probably to enhance safety or to increase efficiency of transport in some way.