Overrun is the pushing force an electric bike continues to give you after you remove pressure from the pedals.
Most ebike drive systems work by sensing a rider’s forward pressure on the pedals and using this as a signal to assist (and multiply) the rider’s inputs with the electric motor.
Overrun can be a hindrance or a help to ebike riders. That depends on how it's mapped into the bike’s software and whether the rider is able to take advantage of it.
What is overrun on an electric bike?

Overrun can be unintentional; on older or less expensive ebikes, it is sometimes a consequence of inferior sensors or less advanced computer software. In these cases, overrun can make the bike more difficult for the rider to control, particularly at low speeds.
Thankfully, modern ebikes are great at managing unintentional overrun issues because clever engineers, using advanced computer technology, are able to minimise overrun and maximise the bio-mechanical interface between the rider and the bike.

However, sometimes overrun is intentional: some high-performance electric mountain bikes have overrun maximised and designed into the bike.
The reason for this is that skilled eMTBers, such as those competing in the now-defunct EWS-E, were able to utilise overrun to save physical exertion, enabling them to be even more effective in conquering fearsome eMTB climbs.
Riders talented enough to use intentional overrun can push the pedals with the bike in the highest power mode, before stopping pedalling and allowing the motor to do the work for them, driving the bike forward.
Although difficult to master, this can give skilled eMTBers the edge over riders on bikes without intentional overrun.
Why do electric bike motors overrun?

If you’re not a global megastar eMTB rider, overrun can still offer you advantages.
The overrun on modern ebikes is mapped seamlessly into the way the motor assists the rider. This means when you’re just starting off on that steep uphill with a fully loaded cargo bike, the momentary dead spots on the top and bottom of the crank rotation are covered by the overrun.
This ‘torque fill’ smoothes out the power delivery to the back wheel of the bike, which equals ease of riding and seamless pulling away.
Is overrun a safety issue?

To the uninitiated, overrun can be intimidating or even frightening, especially given the monster torque on offer from Bosch’s latest remapped 85Nm Performance Line CX motor or DJI’s leviathan 120Nm Avinox motor.
If you accidentally tap the pedal when you’re not on the bike, or even when you’re turning round, the bike can lurch forward unexpectedly or even loop out, leading to concerns that overrun can be difficult to handle for novice riders.
There are no age restrictions on ebikes, and no licence is required before you can ride one; therefore, anyone has the ability to use the powerful bikes mentioned above. Hence concern about whether modern ebikes have become too powerful.