Resonance and length
Antennas work best at resonance — the frequency where the structure naturally ‘rings’ and accepts power most readily.
Standing waves on a wire
Feed a wire with RF and the forward and reflected currents combine into a standing wave. On a half-wave dipole the current is maximum at the centre and falls to zero at the ends, while the voltage does the opposite. That specific length — about half a wavelength — is what makes the antenna resonant and its feedpoint impedance purely resistive.
A handy rule
For a real half-wave dipole, accounting for the slight end-effect of wire thickness:
length (metres) ≈ 143 ÷ frequency (MHz)
A quarter-wave monopole is electrically half a dipole working against a ground plane, so it is half that length.
Off resonance
Away from resonance the feedpoint looks reactive (inductive if too long, capacitive if too short). The antenna still works, but it no longer presents a clean resistive load — which is where matching, covered later, comes in.