Amines are nucleophiles and bases due to their lone pair on nitrogen. Basicity (measured by pKb or conjugate acid pKa) reflects the availability of the lone pair for protonation; nucleophilicity reflects the lone pair's tendency to attack an electrophilic carbon. Aliphatic amines are better nucleophiles than anilines due to electron delocalization in the aromatic ring, while basicity and nucleophilicity trends are not always parallel.
From acid-base chemistry, you know that a base is a species that donates an electron pair to a proton. From your study of amine structure, you know that nitrogen in an amine carries a lone pair of electrons in an sp³ orbital. That lone pair is the source of all amine reactivity — but it can do two fundamentally different things: grab a proton (acting as a base) or attack an electrophilic carbon (acting as a nucleophile). Understanding when an amine does which — and how structural features bias the balance — is the key to predicting amine behavior in reactions.
Basicity is an equilibrium property: how much does the amine want to hold onto a proton once it has one? We measure this by the pKₐ of the conjugate acid (the ammonium ion, RNH₃⁺). A higher conjugate acid pKₐ means the amine is a stronger base. Aliphatic amines like methylamine (conjugate acid pKₐ ≈ 10.6) are moderately strong bases because the nitrogen lone pair is localized and electron-donating alkyl groups stabilize the positive charge on the ammonium ion. Aniline (conjugate acid pKₐ ≈ 4.6) is a far weaker base because its lone pair is delocalized into the aromatic ring — the electrons are partially "borrowed" by the π system and less available for protonation.
Nucleophilicity is a kinetic property: how fast does the lone pair attack an electrophilic carbon? It correlates with basicity in many cases, but not always. Steric bulk around nitrogen reduces nucleophilicity without necessarily reducing basicity much — a bulky base like diisopropylamine is still a strong base (its conjugate acid pKₐ ≈ 11) but a poor nucleophile because the nitrogen is shielded. Conversely, polarizability and solvent effects can make a species a better nucleophile than its basicity would predict. The practical rule is: basicity predicts proton affinity; nucleophilicity predicts carbon-attack rate. When designing a reaction, you choose your amine based on which role you need it to play — a hindered amine like LDA when you want deprotonation without substitution, or a small unhindered amine like n-butylamine when you want nucleophilic attack on a carbonyl or alkyl halide.