Arrhenius acid is a substance which contains hydrogen and prduces H+ ions in aqueous solution.
HCl(aq)→H+(aq)+Cl−(aq)
CH3COOH(aq)→H+(aq)+CH3COO−(aq)
Arrhenius base is a substance which contains OH group and prduces OH− ions in aqueous solution.
NaOH(aq)→Na+(aq)+OH−(aq)
Limitations:
1) This theory is usefull for aqueous solutions only.
2) This theory cannot explain the basicity of substances like ammonia (NH3), sodium carbonate (Na2CO3) that do not contain OH group.