An acid is a species that increases the concentration of the characteristic cation of the solvent. And a base is a species that increases the concentration of the characteristic ANION of the solvent...
So given the context of the acid-base equilibrium that operates in WATER...we know that..
#2H_2OrightleftharpoonsH_3O^+ + HO^-#
And under standard conditions, the extent of the equilibrium is given by:
#K_w=[H_3O^+][HO^-]=10^-14#...at #298*K#, and near #1*atm#.
And from this equation taking #log_10# of BOTH SIDES:
#log_10{K_w}=log_10{[H_3O^+][HO^-]}=log_10(10^-14)#
#-14=log_10[H_3O^+]+log_10[HO^-]#...on rearrangement...
#underbrace(-log_10[H_3O^+])_(pH)underbrace(-log_10[HO^-])_(pOH)=14#
And thus...#14=pH+pOH#
Now a strong acid added to water, i.e. #H_2SO_4#, #HX(X!=F)#, #HClO_4#, #HNO_3#, will produce almost quantitative concentrations of #H_3O^+#..and of course equal concentrations of the counterion.... The equilibrium is always maintained, but the acid increases #[H_3O^+]#, and likewise a base will increase concentations of the characteristic anion #[HO^-]#. Meanwhile a strong base added to water, i.e. #MOH(s)# (#"M=alkali metal"#) quantitatively increases the concentrations of #HO^-#...
Much of this is drawn from Huheey's #"Inorganic Chemistry: Principles of Structure and Reactivity"#, which has an excellent chapter on acid-base chemistry. The account here is in no way a substitute for reading your text and others.