Merrian-Webster defines an interface as:
1 : a surface forming a common boundary of two bodies, spaces, or phases <an oil-water interface>
2 a : the place at which independent and often unrelated systems meet and act on or communicate with each other <the man-machine interface> b : the means by which interaction or communication is achieved at an interface
I think that most people, myself included, first think about an interface as some physical boundary or border. And, that makes sense, because it is much easier to a uderstand a system where you can see all the inputs and outputs. A static structure like a bridge, for example, has inputs in the form of loads on the bridge and outputs in the form of the support it provides.
An example to take a look at is the collapse of the I-35W bridge in Minnesota. The NASA Safety Training Center put out a brief and accessible case study that you can find here.
The report states that the proximate cause of the steel truss bridge failure was the gusset plates at the nodes of the beams. These plates were only half as thick as they should have been based on the original design and anticipated loading. The original model also assumed that the gusset plates were stronger than the beams themselves. Over the course of the years, the bridge's dead load increased due to various maintenance and renovation activities. Even though regular inspections were performed, the gusset plates were reportedly not scrutinized as closely as the beams, because of the assumption that the plates are stronger than the beams. Ultimately, one plate fractured, the beams connected at those nodes shifted, and the structure failed.
This is a good physical example of a physical failure at a boundary (between the beams and gusset plates), but can also be looked at from a systems perspective as far as transition between the system life-cycle phases, from design to long-term maintenance. More on this later.