This was a gag, and it was probably more trouble than it was worth.
Long story short: A "tachyon communicator" is basically a radio that can communicate instantly even when you are millions of miles apart. Don't worry about the rest.
If you still want the long, nerdy version: A tachyon is “a hypothetical particle that travels faster than light” (in the words of Wikipedia). The term was coined in an academic paper back in the 1960s, and made its way into sci-fi in the meantime.
Sending messages faster than light could come in handy for spread-out space explorers, as light takes a decently long time to reach across an entire solar system. For instance, if you were to use a powerful radio here on Earth to talk to somebody in orbit of Neptune, it could still take 4 hours for your words to reach them at the speed of light. With a tachyon communicator, though, there's no such "in-system lag" (i.e., no delay in communicating with somebody in the same solar system), as tachyons move faster than light.
So what's up with the rest of that line in Cosmic Highway? ("When used in the same room, signal plays a split-second before you speak.")
The part about being in the same room is a joke based on my (admittedly limited) understanding of Einstein's theory of relativity: If you break the speed of light, you go back in time. Or, if I may steal fromWikipedia again, "Faster-than-light communication is, according to relativity, equivalent to time travel."
Now, as an aside: Have you ever used a cell phone or a walkie talkie to talk to somebody in the same room as you? There's a funny little delay between your voice coming out of your mouth and then coming out of the other person's device.
The joke is that tachyon communication devices have that delay too, but in the opposite direction — what you’re about to say comes out the other end a half-second before you say it.
Now, you may be wondering: Why would I devote so many words worth of precious page-layout real estate to a joke maybe half a dozen readers will even get?
The answer is: Because I am a huge dweeb. (But I am hoping from your screen name that we share this in common.)