1) The lone pair of electrons on the nitrogen of the ammonia will attack the delta positive carbon in the carbonyl group the benzoyl chloride (forming a bond between the nitrogen and the carbon) [ADDITION]
2) The electron pair in the pi bond between the carbon and oxygen will move to the oxygen atom, causing it to become negatively charged.
3) The electrons on the oxygen will then reform the double bond, whilst the electrons in the covalent bond between the carbon and the chlorine will move onto the chlorine atom, such that it becomes Cl- and is no longer part of the moelcule. [ELIMINATION]
4) To rebalance the positive charge on the nitrogen (it originally formed a dative covalent bond with the carbon atom), the electron pair between itself and one of its hydrogens will move onto it. The lone pair on the Cl- ion will then form a dative covalent bond with the released H+ ion.
and so the substances benzamide (C6H5CONH2) and HCl will be formed.
In essence, this is a nucleophilic substitution reaction, where the ammonia, with its lone pair of electrons, is the nucleophile.