Here's a quote explaining how it works from the Cambridge University release ben_watkins supplied:
"The inerter looks superficially like a conventional shock absorber, with an attachment point at each end. For example, one end may be attached to the car body and the other to the wheel assembly. A plunger slides in and out of the main body of the inerter as the car moves up and down. This causes the rotation of a flywheel inside the device in proportion to the relative displacement between the attachment points.
The result is that the flywheel stores rotational energy as it spins. In combination with the springs and dampers, the inerter reduces the effect of the oscillations and thus helps the car to retain a better grip on the road.
Though they remain the preserve of F1 for now, inerters have many other potential applications. In time, they could extend far beyond the realm of motorsport and be incorporated into conventional road vehicles and motorcycle steering systems, to name just two areas."
You may remember checkered kindly supplied links - which document the development of the inerter all the way back to 2002 - see his post from May 20th 2008:
The titles of the papers are quite specific:
Synthesis of Mechanical Networks: The Inerter
The Inerter Concept and Its Application
Performance Benefits in Passive Vehicle Suspensions Employing Inerters
Positive Real Synthesis Using Matrix Inequalities for Mechanical Networks: Application to Vehicle Suspension