The volume around a star in a binary system in which, if you were to release a particle, it would fall back onto the
surface of that star. A particle released above the Roche lobe of either
star will, in general, occupy the circumbinary region that
surrounds both stars. The point at which the Roche lobes of the two stars
touch is called the inner Lagrangian point.
If a star in a close binary system
evolves to the point at which it fills its Roche lobe, calculations predict
that material from this star will overflow both onto the companion star
(via the L1 point) and into the environment around the binary system.