Build refers to a character's skills and equipment, when coordinated to achieve a desired goal or play style. A strategy. Examples of popular builds are the Spin2Win barbarian, the Archon Wizard, or the Tempest Rush Monk.
Most builds are cookie cutter, meaning that they are popular and often recreated by players following the same rough (or exact) skill arrangement and general equipment goals to achieve a successful killing speed.
Builds can be optimized for farming, rushing, key running, high MP grinding, PvP brawling, or various other purposes, and many players take advantage of Diablo 3's freespecs system to change their characters around regularly, re-purposing them by changing around some skills and gear to change their function. This is known as rebuilding or respeccing.
For instance, most characters need higher resistances and hit points to survive on higher MP levels or in a multiplayer game, so players will change around some equipment, stick an amethyst in the helm socket, switch some passives, etc, while retaining most of their normal skills and gear.