The Bergenholm was device created by two scientists, Rodebush and Cleveland, and perfected by a third, Nels Bergenholm. It works neutralising all of the inertia of an object, such that the only limit to its maximum velocity is when the thrust provided by its engines equals the resistance of the medium it is travelling through. This allows Lensverse ships to travel at FTL speeds whilst remaining in ordinary space, although aside from feelings of nausea (not dissimilar to how one feels when weightless) and the need for people to behave differently in order to move about in an inertialess environment, it does not appear to have any of the issues that true inertialessness would have on objects (likely to be death in the case of people for example).
Starships which are inertialess are referred to as "free", whilst those with inertia are "inert". There have been experiments to develope negative inertia, but none have been successful. In addition, the Nevians in Triplanetary also had a drive that only partially neutralised inertia, and which still permitted FTL travel, but which has not been seen since that book.
Bergenholms are also found on the personal armoured space suits used by the Galactic Patrol, and likely by Boskonian equivalents as well. These are capable of sending someone along at several times the speed of light over interplanetary distances.
Conservation of Momentum
When a Bergenholm is activated, the ship's "intrinsic velocity" (the velocity at that moment) is suspended, and the ship becomes inertialess. When the ship becomes inert once more, it immediately regains the intrinsic velocity it had prior to becoming free. This can make for dangerous situations if your pilot forgets to correct his intrinsic velocity after travelling to a new planet.
As A Defence
Aside from permitting FTL travel, the Bergenholm also provides an impromptu means of defence against most forms of attack. Because missiles, beam weapons and the like all impart momentum onto the object they strike, unless they are exceptionally powerful (and possibly FTL in nature as well), the resistance provided by the near-vacuum of open space is so low that a ship struck will quite simply be pushed back by the attack, rather than damaged.