What do you understand by the statement ‘acetic acid is a monobasic acid’?

Hint: Acidity or acid strength is based on how easily an atom is able to give an electron or an ${H^ + }$ ion. The strength can be defined on the term of basicity, as to how many hydroxide ions can come and replace the total numbers of protons that are available in the acid. This quantification of basicity gives rise to terms of monobasic, dibasic, or tribasic.

Complete answer:
First of all, we need to understand what acidity or basicity is. Acidity is defined as the tendency of any molecule to donate a proton in water easily. Now based on how easily a compound is able to donate the proton, the acidity or the acidic strength is defined on.
The number of ${H^ + }$ ions that are donated or that are given by the molecule when added to water gives the value of its basicity. Basicity is defined as the number of ${H^ + }$ ions given by the molecule when it is added into the water molecule.
When we add acetic acid into water, it dissociate in the following manner:
$C{H_3}COOH \to C{H_3}CO{O^ - } + {H^ + }$
We can see that it gives off only one ${H^ + }$ ion when added to the water. Hence, acetic acid is termed monobasic acid.

Note:
Few other examples of monobasic acid include hydrochloric acid, nitric acid, etc. sulphuric acid is a dibasic acid since it gives off two ${H^ + }$ions and sulphate anion. Thus, in order to answer the given format, one must always take care of the definition. The above question can be answered only when the concepts to basicity are clear.