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.
Note the symbols after each compound, these are state symbols which represent the state of matter that the compound is currently in.