I am a business developer who is new to game programming. In learning Stencyl, I see that there are things called collision shapes associated with tiles. This seems to be a standard term in game programming. What is a collision shape?
A collision shape is the shape of an object as "seen" by the collision/physics engine.
Think of a square box and a circle:
Near the corners, objects will hit or collide with the box but not the circle even though the height and width of the objects are identical.
More complex shapes as also possible. Circles/spheres are the simplest (and fastest) but tend to poorly represent many kinds of objects. Axis-aligned bounding boxes (AABBs) are the next most common/efficient. Capsules (a cylinder with half-spheres on each end) are common for characters. The common collision algorithms all support convex hulls (a polygon/polyhedron with only convex angles), and decent physics engines are typically capable of dealing with objects which have multiple shapes (allowing for objects to incorporate shapes with concave features, even though the collision engines typically can't handle them directly).
Tiles will typically be a simple square AABB fixed to a grid. Specialized collision engines may have direct support for tiles, since a grid-aligned fixed-width AABB is even easier to deal with than arbitrarily positioned/sized AABBs.