I like to offer a different definition for nucleophilicity. Often there is confusion between the terms nucleophilicity and basicity, esp. when the same anion / molecule having “lone pair” of electrons – behaves as both. In both cases, an electron pair is donated. So, I would term nucleophilicty as:
“the ease of forming a bond with carbon” – as practically all nucleophilic reactions result in a C-Nu (Nu = nucleophile) bond formation.
[Basicity would be the ease with which an anion / molecule (could be same as above) can pick up an acidic proton... or simplifying, to form a bond with hydrogen only]
The explanations for order of basicity is already well explained by Ms. Aarti & Mr. Rishi. Simplifying, we can say that the order of nucleophilicity increases from “right to left” in the periodic table (& thus is inversely proportional to the electronegativity of anion / molecule)