Primary aromatic amine comes in its salt form, and in the salt form the aromatic amine cannot react with acetic anhydride. Sodium acetate being a weak base is used in the reaction so that small amount of free aromatic amine is regenerated and reacts with acetic anhydride.
For instance, in the reaction between aniline hydrochloride and acetic anhydride, sodium acetate is added to the reaction as it helps to release free aniline from its salt form to interact with acetic anhydride to form acetanilide.
NaOAc is a base here. Any amine often have tendency to take proton from reaction medium which can decrease it's nucleophilic nature. You can use Na2CO3 in the place of NaOAc.
Dear Noha, as mentioned in your question, a good method for acetylation of aromatic amines in aqueous medium involves using the amine-hydrochloride, a concentrated solution of sodium acetate and acetic anhydride. The idea behind this is to be able to carry out the reaction in aqueous solution. Under these conditions the sodium acetate acts as a weak base and liberates the free primary amine which immediately reacts with the acetic anhydride. The big advantage of working in aqueous solution is that the pure acetylated product precipitates dierctly from the reaction mixture. In this context please also have a look at the Open Access paper entitled "Mild and eco-friendly chemoselective acylation of amines in aqueous medium" which was published in ARKIVOC 2004 (i) 55-63. This paper can be freely downloaded as pdf file from the general internet. It reports the use of NaHCO3 instead of sodium acetate as a mild base.
Sod acetate in presence of released acetic acid, product of an initial acetylation step form a buffered pH medium. The resultant buffered pH might keep an equilibrium between the amine ( unionized) and its conjugate acid (protonated base) which direct the reaction to completion i.e further acetylation of the amine. I hope that this will add to the above answers.