To switch stations simply means to go from one language to next during your interaction with another speaker who may also be bi or multilingual. People "switch stations" to add a bit of context on the subject matter or topic they're talking about so that the listener can fully comprehend the speaker. The speaker also does this as a way to relate to their listener(s) and make them feel connected. The phrase/term originally derived from the multitude of radio and TV stations, in South Africa, that are being broadcasted in different tongues/languages for specific listeners/viewers to read. So if you change from one station to the next, you would hear the new speaker on your telly or radio speak in a different tongue than the predecessor from the other station.
Speaker #1: Sawubona bhuti. Igama lami nguSphiwe and what is your name?
Speaker #2: Yebo, sawubona Sphiwe. I'm Trevor.
Speaker #1: Oh, okay. Ngiyajabula ukukwazi Trevor.
Speaker #2: ð
Yebo. Nice to meet you too, Sphiwe.
(Example of two speakers switching stations between each other)