In order to understand the difference between Molecule and Formula Unit lets take one one example for each.
NH₃ :
Ammonia is a covalent compound which contains three covalent bonds between N and three H's. One molecule of Ammonia can exist independently, so it is possible to find a single molecule of NH₃ comprising of one nitrogen and three hydrogen atoms bonded covalently.
NaCl:
Sodium chloride is made up of Na⁺ and Cl⁻ ions. Now, the formula NaCl is not molecular formula, instead it is a formula unit. Formula unit means that this compound consists of giant structure of Na⁺ ions and Cl⁻. There numbers can not be counted but the ratio of these two ions to each other is countable and for each Na⁻ ion there is one Cl⁻ ion. Hence, Formula unit is an Empirical formula of any Ionic compound.