Play two notes that are very close in frequency — say 440 Hz and 442 Hz. You'll hear a wobble: the volume rises and falls 2 times per second. That's a 'beat'.
close frequencies → beats: the sum swells and fades |f₁ − f₂| = 1 time per cycle (dashed envelope)
Why two waves make a wobble
Add two sine waves whose frequencies are close and they drift in and out of step. Where the crests line up, the sound is loud; where a crest meets a trough, they cancel and it's quiet. That slow loud-quiet-loud cycle is the beat, and it repeats |f₁ − f₂| times per second.
You play 440 Hz and 443 Hz together. How many beats per second do you hear?
To tune by ear: play your note against a reference, listen for the wobble, and adjust until the wobble slows to nothing. Zero beats means the frequencies match.
The wobble rate equals the difference in frequencies.
Piano tuners use beats. They listen for the wobble between two notes; when it stops, the notes are perfectly in tune.