A tooth is built from four tissues. Three are hard, calcified tissues: enamel, dentin, and cementum. The fourth, the pulp at the center, is soft tissue containing nerves, blood vessels, and connective tissue.
Enamel is the hard outer layer covering the crown. Because it contains no living cells, it cannot repair damage from decay or wear. Dentin lies beneath the enamel and cementum and makes up the bulk of the tooth; it has tiny tubules, so exposed dentin can make a tooth sensitive to heat, cold, or sweets. Cementum is the hard tissue covering the root, and it anchors the periodontal ligament that holds the tooth in its socket.
Source: American Dental Association (MouthHealthy) — Tooth anatomy
Image: Tooth anatomy illustration by BruceBlaus (Blausen Medical), CC BY 3.0, via Wikimedia Commons.