In this franchise all immortals have what's known as The Buzz, a type of extra sensory perception that "goes off" in the presence of another immortal. It seems to be a sound or vibration that happens in their head, similar to Peter Parker's Spider sense. However, unlike that early warning system, its very, very general; it seems to work within about 50 -100 feet, but isn't very specific; two unknown immortals may get a "Feeling" about someone, having grown accustomed to their fellows showing up randomly, and knowing what signs to look for... but they wouldn't [by all indications] be able to "pick each other out" specifically of of a crowd, sight-unseen.
The Buzz also doesn't seem to produce any other physical effects, nor does it get louder, stronger or weaker as an immortal gets closer or further away. Effectively, it's just an early warning system that let's them know another is near, so they can't be sneak attacked. As a narrative tool, it's pretty clever; its a nice way to even the playing field and wonder why the Game didn't end centuries before. I think, though this is speculation, that this is an more refined extension of the "Connection to everything" that Rameriez was trying to teach Connor MacLeod to explore when he first became an immortal.
William Panzer was part of Davis-Panzer Inc, the production company behind the Highlander franchise. He co-wrote screenplays for three Highlander films, and was the Executive Producer for Highlander: The Series. In an interview on the 2001 bonus material of the series season 1 DVD, Panzer defines the Buzz as:
a concept of Immortals being able to sense each other's presence from a reasonable distance. We called it the Buzz. That word was never used, but that's how it was featured in the scripts.
It's further expanded upon in the Fan wiki, based off interviews and DVD extras: