I've been watching some cooking videos and frequently the chef would say that something he cooked was a "rustic" dish eg. "rustic pot roast"? What does rustic mean?
There's no standard definition - it's a descriptive term, not a standardized culinary one. In practice, it's often used in fine-dining contexts to denote a deliberately less subtle or carefully assembled dish. Stews are often considered "rustic", in contrast to highly precise cuisine like sushi. A loaf of irregular sourdough bread might be called "rustic" in contrast to a croissant. It's often meant to imply a focus on flavor, simplicity, and familiarity rather than on appearance, originality, or technique.
It's a somewhat disingenuous term in that it's often used by and applied to professionals who focus overall on fine cuisine. It implies something that could have been made with much finer precision and presentation, but was kept deliberately rough. A Michelin-starred chef's chili con carne might be considered "rustic"; your grandmother's chili made with ground beef and tomato paste probably wouldn't be. A roadside barbeque shack's brisket isn't necessarily "rustic", but the same beef cooked and plated in a high-end restaurant would be.
That all said, it bears repeating that this isn't a consistently applied term. It's used in the same way as words like "classic" or "artisanal" - because it sounds good to diners and conveys an impression of simple quality, not because it means anything specific in regards to preparation.
I'd like to start by showing you this page of knife cuts. Not to teach lessons about cutting but to illustrate a point. Look how each cut has a flat surface (even on potatoes and carrots). However I have worked in kitchens where even some of those would be thrown out. Perfection can be paramount in some places. Even in the bars I've worked at cut consistency is fundamental.
What does this have to do with anything?
In my experience Rustic is homestyle. Rustic is less professionally demanding. Rustic might have the occasional minor flaw that high class standards would not allow. Rounded potatoes and carrots, and vary cut sizes.
Rustic dishes don't usually have very advanced techniques but I would not go so far as to limit them to only the simplest of techniques.
There is also a subset of the term Rustic that mimics dishes that are frequently made in a homestyle manner but with an interesting and fancy technique added for (well lots of reasons: flair/ artistry, taste, presentation, novelty (all of those if the chef is truly skilled)).
I also once heard Mario Batali on "Molto Mario" say any chef who used the word "rustic" was probably being lazy.
Usually, a more "rustic" presentation will have things chopped rather than minced with no more complex sauces than a simple reduction sauce and often served in its own ceramic cooking vessel.