Abeam is a term used in aviation to describe the positioning of an aircraft directly across from or over a NAVAID (navigational aid) or any other type of fix. A fix can be an airport, tower, waypoint, or any notable natural or man-made geographical object.
Often, "Abeam" will be used to describe a pilot's position directly across from or over a NAVAID. A NAVAID can be a VOR (very high-frequency omni-directional range beacon), an NDB (non-directional beacon), or a GPS waypoint. In order to be abeam, you have to have instrument confirmation that you're next to it. In a VOR, this is commonly shown by the shaking of the CDI needle. The CDI needle in an aircraft VOR instrument shows the direction to, from, left, or right of the NAVAID.
With a GPS waypoint being abeam, a fix would be shown by an indication on the GPS screen, and with an NDB, it would be shown on the ADF (automatic-direction finder) instrument with an arrow pointing to the side of an airplane or completely reversing in direction. Abeam a fix can be noted either visually or by instruments. So, depending on the type of aircraft and equipment available in that aircraft, whether abeam a fix or not, will be found in different ways.
A pilot can be asked to perform special instructions or report their position to traffic control (ATC) when abeam a fix in cases where the controller is providing positive separation to aircraft or when performing special approaches. When a pilot is holding over a fix or NAVAID, then being abeam of a point plays an important role. In order to fly a correct holding pattern, the pilot must be able to track a course to and from the NAVAID or fix it correctly. They must make their turns to perform the holding patterns at the right times, and being abeam the NAVAID/fix determines those turns.
Also, when a pilot is traveling using the help of an airway, they might be required to change courses to follow a different NAVAID. Being abeam the NAVAID usually indicates a course change.