... transfer in highly elliptical orbit (HEO) or a distant retrograde orbit (DRO) around the Moon on both the outbound and return legs. This saves taking about 20 metric tons of mass to and from Mars, and allows for some hardware reuse on later missions.
The basic idea is to stage components of a large manned mission in a high Earth orbit, where you have already imparted the majority of the energy needed to get to destinations in the solar system. The $\Delta V$ to get from LEO to a high-Earth orbit with an apoapsis at the distance of the Moon is 80% to 85% of the $\Delta V$ to get from LEO to Mars.
You can use highly efficient electric propulsion systems to get to HEO, since you don't care how long it takes for uncrewed components to get there, in order to minimize the launch mass, and thus the cost. These can be fueled chemical propulsion stages, habitats, and other pieces. Our Moon then provides a convenient and nearly free means to both raise and drop components' periapsis for storage in a circular HEO, rendezvous with a crew, and to use a low periapsis for a near-Earth chemical propulsive maneuver for efficient injection to an interplanetary trajectory.
See this article for an overview of the concept.
A stable way to store such pieces is in a DRO around the Moon, which is energetically cheap to get into and out of from HEO. You can also put some of your returned hardware, such as your deep-space habitat, in DRO for resupply and reuse.
You never heard of Distant Retrograde Orbits because they were never before utilized. Quoting Kirstyn Johnson's (Colorado Center for Astrodynamics Research, University of Colorado at Boulder) work titled Understanding NASA's Asteroid Redirect Mission, article on Distant Retrograde Orbits:
Currently, research has not revealed a spacecraft that has utilized a Distant Retrograde Orbit in its operation, despite 40-50 years of research going into this topic. The proposed JIMO mission [Jupiter Icy Moons Orbiter], before it was cancelled in 2005, was looking into using a DRO for its stability and low-energy transfer qualities. DROs have also been of interest to potential spacecraft in creation of an initial warning system for large coronal mass ejections heading towards Earth. However, neither of these missions came to fruition. Therefore, there is not mission experience in flying a spacecraft to and into such an orbit.
Some of the benefits of such orbits are avoiding instabilities of closer orbits due to third body gravitational perturbations (a term “quarantine orbit” is mentioned therein and referring to Lyapunov stability), and lower required delta-v for orbital transfers, but come with a caveat that:
Due to the retrograde then prograde motion of the orbit in the inertial frame, a satellite's motion cannot be described by Keplerian orbital elements, making the problem more difficult to analyze.
Refer to the mentioned article for more detailed explanations and images helping visualize benefits and difficulties of using DRO.