What it is
Claves are two sticks of hard wood. One rests on a cupped palm, which works as a resonator, and the other strikes it. The sound is dry and high, and cuts through the whole band.
The rhythm played on them has the same name: five strokes over two bars. All of salsa is built on it: piano, bells and horns are written "in clave", so their parts fit it.
The strokes
There's one stroke: stick on stick. What matters is not how but when: three strokes in one bar, two in the other.
In 3-2 the three come first (1, the & of 2, 4), then the two (6 and 7). In 2-3 it's the same figure started from its second bar: two, then three.
Rumba clave differs by one stroke: the third stroke of the three-side moves from 4 to the & of 4. The rhythm pulls more — it's what rumba guaguancó is played in.
What a dancer hears
In a song you often can't hear the clave, but the whole band holds on to it. The strokes on 6 and 7 in 3-2 land with the steps of the basic's second half — a good landmark.
If the band's accents don't seem to fit the count, listen for where the clave has three strokes and where two: 3-2 and 2-3 sound different, though the dancer's count stays the same.