A "wavepacket" is simply a single composite wave made up of two or more individual waves combining with each other in a consistent fashion over time. Wavepackets are an important concept in quantum mechanics. For an electron, atom, molecule, or any other quantum system, an individual quantum state can be represented as a stationary or "standing" wave whose points of maximum disturbance (peaks and valleys) and points of minimum disturbance (known as nodes) stay fixed.
When a group of individual quantum states (right) add together, they combine to form a wavepacket (left). Under certain conditions, the resulting wavepacket can consist of a single peak (as depicted on the left)--causing the quantum system to act as a particle in a well-defined state, instead of the more customary quantum wave spread out in space.