Strong acids completely ionise or dissociate in water, whereas weak acids partially ionise in water.
Hydrochloric acid is a commonly used strong acid which completely dissociates in water as shown by the below equation:
HCl (aq) → H⁺(aq) + Cl⁻(aq)
The equation demonstrates that hydrochloric acid breaks down (dissociates/ionises) into its component ions in the presence of water.
An example of a weak acid is carbonic acid and as shown by the equation below, it only partially dissociates in water:
H₂CO₃ (aq) ⇌ 2H⁺(aq) + CO₃²⁻(aq)
The equation shows a partial dissociation of carbonic acid to its ions, this is demonstrated by the reversible reaction symbol that tells us the reaction is continuously going back and forth.