The fascia is the board along the edge of the roof, and it is what your gutter is fastened to. When an old gutter leaks at its seams or overflows for years, the water runs behind it and soaks that board. In Florida heat and humidity, wet wood rots fast, and termites and carpenter ants are happy to help.
Signs to look for: paint peeling along the roof edge, wood that feels soft when pressed, a gutter pulling away from the house, or gaps where the soffit meets the fascia. Any of these means the gutter has nothing solid left to hold on to.