A DXF file is a vector drawing: a set of instructions describing lines, arcs and curves rather than a grid of pixels. If you have downloaded a cut file bundle, there is almost certainly a .dxf in it next to the SVG, and it is the file that rescues you when the SVG will not import.
The short version: DXF is the format to reach for on the free version of Silhouette Studio, which does not import SVG. Everything below is the longer version.
Where DXF came from
DXF stands for Drawing Exchange Format. Autodesk created it in 1982 so that drawings made in AutoCAD could be opened in software that was not AutoCAD. That origin explains almost everything crafters find odd about it.
It was built for engineering drawings, so it is very good at describing precise outlines and rather poor at describing decorative things like fills, gradients and transparency. A DXF knows exactly where a line goes. It often has no opinion at all about what color the shape should be.
It is also a plain-text format. You can open a DXF in a text editor and read it, which is why it survived forty years of software changes: anything can be taught to read it.
What is actually inside one
A DXF holds entities and layers.
Entities are the drawing pieces: lines, arcs, circles, and polylines, which are the connected sequences of segments that most cut shapes are made from. Your machine turns each of these into a blade path.
Layers are the grouping mechanism. In a well-made craft DXF, each color of the original design becomes its own layer, so you can cut the layers from different sheets of cardstock. In a badly-made one, everything lands on layer 0 and arrives as a single tangle.
What a DXF usually does not carry is fills. An SVG can say "this shape is filled with coral pink". A DXF mostly just says "here is the outline". This is why a design that looked solid in the preview opens as a wireframe, and it is normal rather than broken. Your machine cuts the outline either way.
