A unibody car has a rigid body assembly that sub-assemblies like the front and rear suspensions are hung off of.
Here's the only decent picture of a unibody I could find.
As previously stated, the Mustang has been a unibody car since day one.
The alternative to a unibody is what is called body on frame, where a frame is built out of steel rails supported by cross members. Then the body is set on top of that.
thats why people install subframe connectors. the font and the rear are fairly rigid "subframes" but the center of the car does not have as much support. its mostly just sheetmetal. subframe connectors tie the front and rear together so its stronger overall.