An arrow in the literal sense is a projectile designed to be fired from a bow at a fixed or moving target, often used in hunting or contests of sport. In a more broad sense, an arrow refers to any directional symbol that offers guidance as to the path one should follow (often used in signage, painted on roads, etc.).
In the project management arena, an arrow refers to the presentation of a schedule activity in a graphical format through use of a logical relationship between schedule activities in the precedence diagramming method or, more commonly perhaps, the arrow diagramming method. Arrows can be used to illustrate periods of time in some uses, such as in reference to the gap of time that it will take to move from one schedule event to another. Or, when used in a less detail oriented chart or display, can merely be a way to illustrate graphically the order in which schedule events are expected (and in most cases are required) to take place in order to get from the start of a project to the desired endpoint.
This term is defined in the 3rd edition of the PMBOK but not in the 4th.