An AC waveform consists of a (ideally, mostly) sinusoidal waveform that crosses zero voltage and current periodically.
All wiring has stray inductance, and when contacts are opened the inductance will cause a rise in voltage until there's an arc across the contacts.
There's plasma in the arc that makes the impedance between the contacts much lower than air, meaning the arc will tend to continue as the contacts move further apart.
With the AC waveform, the current crossing zero will extinguish the arc.
With DC, there's no zero crossing, so the contacts are limited to a much lower voltage so that the there's not enough electric field to keep the arc "lit" while the contacts pull apart.
Excess arcing is very damaging to the contacts, and will destroy the breaker if not controlled by observing the ratings.
There are special breakers and relays for higher voltage DC that use various techniques to interrupt the arc like magnetic coils to blow out the arc.
Interrupting DC is harder because there's no zero crossing to extinguish the arc. Therefore there's a lower electric field rating across the contacts for the same contact configuration.