Strong acid : The mineral acids like hydrochloric acid $(HCl)$, sulphuric acid $\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)$ and nitric acid $\left(\mathrm{HNO}_{3}\right)$ when dissolved in water, they get completely ionised.
The acid which gets ionised completely when dissolved in water is known as strong acid. For example,
$(1) \mathrm{HCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{Cl}^{-}(a q)$
Thus, in $1 \mathrm{M} \mathrm{HCl}$ aqueous solution, concentrations of $\mathrm{H}_{3} \mathrm{O}^{+}$acid $\mathrm{Cl}^{-}$are $1 \mathrm{M}$.
$(2) \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{SO}_{4}^{2-}(a q)$
Thus, in $1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ aqueous solution, concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$and $\mathrm{SO}_{4}^{2-}$ are $2 \mathrm{M}$ and $1 \mathrm{M}$ respectively, because two moles $\mathrm{H}_{3} \mathrm{O}^{+}$are formed by ionisation of one mole $\mathrm{H}_{2} \mathrm{SO}_{4}$.
In the aqueous solution of strong acid, total solute substance is in the form of ions, i.e., the solute substance is ionised to $\mathrm{H}_{3} \mathrm{O}^{+}$.
Weak acid : The organic acids like acetic acid (in vinegar), lactic acid (in curd, buttermilk), citric acid (in lemon, orange), tartaric acid (in tamarind), oxalic acid (in tomato) when dissolved in water they get partially ionised.
The acid which gets ionlsed partially or incompletely when dissolved in water is known as weak acid.
For example, The concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$is not $1 \mathrm{M}$ in $1 \mathrm{M}$ $\mathrm{CH}_{3} \mathrm{COOH}$ aqueous solution but it is very less. (approximately $2$ to $3 \%)$