probability density
Picture a fine mist sprayed across a room — thick and milky in some corners, thin and clear in others. If you reached out and grabbed a small handful of air, you would most likely catch mist where it is thickest. Probability density is exactly this idea for a quantum particle: a map over space whose thickness tells you, at each spot, how likely you are to find the particle if you look there.
More precisely, probability density is the square of the magnitude of the wavefunction. The wavefunction itself can be negative or complex, but squaring its size always gives a positive number that behaves like a real, physical concentration of likelihood. To get the actual chance of finding the particle within some region, you add up (integrate) the density over that whole region. Where the density is high, the particle is likely; where it is zero — at a node — the particle is never found.
The honest qualifier is the word density. The probability density at a single mathematical point is not itself a probability — it is probability per unit volume, like how mass density is mass per unit volume. Only when multiplied by a volume does it become an actual chance. For chemistry this map is everything we mean by an electron cloud or electron density, and it is what bonds, reactions, and X-ray crystallography ultimately measure.
The 1s probability density of hydrogen is densest right at the nucleus and fades smoothly outward. But if you ask instead at what distance the electron is most likely to be found, the answer is a shell about one Bohr radius out — because although each point near the nucleus is dense, there is far more total volume in the shells further away.
Densest at the nucleus, yet most likely found a shell out — volume matters.
Probability density and the radial distribution (probability per shell) are easy to confuse. The first peaks at the nucleus for a 1s orbital; the second peaks a short distance away, because it weights each shell by its much larger surface area.