Organic chemistry and human beings both pursue betterment and advancement.
Humans engage in welfare activities to improve the well-being of others, tackle inequality, and create strong bonds. The same principle is also observed in organic chemistry.
Some species are rich in electrons, and they help their electron-deprived counterparts by donating their electron richness and taking away their electron imbalance, thereby forging a new bond. However, in the context of organic chemistry, this new bond is real and manifested as a covalent bond. Here, the electron-rich species that donate the electrons are called nucleophiles, and the receivers are the electrophiles.
The nucleophile derives their electron prosperity from three different sources: lone pair, pie bond, and, on rare occasions, sigma bond.
A few examples are-

They may wear a mask to remain unidentified or neutral in charge or walk exposed as negatively charged agents of change.
Therefore, within the purview of organic chemistry, one can define a nucleophile as an electron-rich species, either neutral or negatively charged, that can donate an available pair of electrons to an electrophile, forming a covalent bond.
Role of a Nucleophile in a Chemical Reaction
In a chemical reaction, the nucleophile constantly seeks its complementary partner, the electrophile. The nucleophile then donates its two electrons to the electrophile and forms a new covalent bond.
Electrophiles are electron-deficient due to multiple factors; the most common is electronegativity.
Due to electronegativity, an electronegative atom or group of atoms takes away a covalent bond’s electron density, due to which one atom in the bond is richer than the other in electrons. This creates two terminals: electron-rich and electron-poor, called the dipoles.
For example, in a molecule of CH32-CH21-Br, the Bromine (Br) is more electronegative than Carbon 1 to which it is directly attached. The Bromine pulls most of the electron density of the bond and makes the adjacent Carbon 1 more electrophilic. This loss in electron density is denoted with a partial positive charge on Carbon as (δ+), and the gain is represented with Bromine (δ-).
CH3-δ+CH2-δ-Br
The carbon 1 with the partial positive charge becomes the electrophilic center. In a chemical reaction, the nucleophile is attracted to such an electron-deficient center, where it will donate the electrons and form a new bond.

The electronegative atom that earlier caused the bond to weaken due to the electron pull is lost as a leaving group (here, Br-), taking the two bond electrons with it.
Note that a curly arrow always travels with two electrons. (Read more about the use of double-headed curly arrow in Types of Arrows in Chemistry).
Some of the other factors responsible for creating electrophilic centers are- electron delocalization (resonance), presence of empty p-orbitals, Carbon atom next to positively charged Oxygen and Nitrogen, etc. The nucleophiles approach these centers in bond formation reactions.

Next: Type of Nucleophile - Lone Pair
Next: Type of Nucleophile - Pie Bond
Next: Type of Nucleophile - Sigma Bond
Next: Periodic trend and Order in Nucleophilicity
Next: Nucleophile Reactions - Displacement Type
Next: Nucleophile Reactions - Addition Type
Next: Ambident Nucleophiles
Blogs - Common mistakes while learning about the nucleophiles
Techniques to identify a nucleophile – Visual Inspection Method - Part 1
Techniques to identify a nucleophile in organic reactions – Following the Arrow Trail
