The term interface in Foldit most often refers to the area where two or more protein chains or ligands bind together to form a single unit or complex.
In binder puzzles, goal is to design a binder with a strong interface to a target protein. Various binder metrics, such as DDG, SASA, and shape complementarity may be used to guide design. The Foldit blog post Analysis of protein binder designs gives more backgrounds on these metrics.
The basic concepts of filling voids, hiding exposed hydrophobics, avoiding buried unsatisfieds, and making hydrogen bonds still apply to interface design.
In symmetry puzzles, there's often a "Core: Complex" objective, which is one way of looking at the interface between symmetric chains. The "Core: Complex" objective may offer a bonus or a penalty depending on how many segments are in the complex. In other cases, "Core: Complex" does not affect the score, but does identify which segments.
Clicking the "Show" option for the "Core: Complex" objective changes the coloring. Segments in blue are not in the core, segments in orange are in the core, and green segments are on the border with this coloring.
In symmetry puzzles involving a hydrogen bond network objectives, there may be a restriction that only segments in the complex core can participate in a network.