An acid anhydride is what you get if you remove a molecule of water from two carboxylic acid -COOH groups. For example, if you took two ethanoic acid molecules and removed a molecule of water between them you would get the acid anhydride, ethanoic anhydride (old name: acetic anhydride).
Acyl chlorides (also known as acid chlorides) have the general formula RCOCl. The chlorine atom is very easily replaced by other things. For example, it is easily replaced by an -NH2 group to make an amide.
The carboxylic acid is first converted into an ammonium salt which then produces an amide on heating. The ammonium salt is formed by adding solid ammonium carbonate to an excess of the acid.
The hydrolysis of nitriles is a satisfactory method for preparation of unsubstituted amides and is particularly convenient when hydrolysis is induced under mildly basic conditions by hydrogen peroxide.