Subframe connectors are metal braces that weld to the front and rear subframes, tying the two assemblies together. All late-model mustangs have fairly strong front and rear subframe assemblies, but being unit-body construction cars, the subframes are an integral part of the car's body, rather than being part of a separate frame as on many older cars from the '50's and '60's. There is no real "frame" underneath the car between the front and rear "subframes" - your car is basically held together by the sheet metal and spot welds in the floor pan/transmission tunnel/rocker panels! (in coupes, the roof helps, too.)
What this means is that over time, as mileage builds (and especially if you drive hard and/or add power), the car becomes more flexible as welds weaken and the metal itself becomes more flexible from being twisted from the torque of the drivetrain and from going around corners. This is why all such mustangs (especially convertibles) squeak and rattle as they get older. Also, in day-to-day driving, even a new car sometimes feels a bit unstable over bumps, and tends to flex under hard cornering.
Later convertibles have bolt-in subframe connectors, but they don't do a lot of good - a good subframe connector should be welded in, and a lot of them bolt to the floor pan using the seat attachment bolts, adding extra strenth to the assembly. Do a search on this site and you'll find a lot of good advice on installation (whether you do it yourself or have a shop do it) and on brands.
All in all, subframes are a good investment. Not only will you notice an improvement right away in how the car feels (especially in curves and over bumps), but you are insuring your car against long-term deterioration in ride quality and handling, not to mention against squeaks and rattles. Plus, they are a good foundation for further power/suspension improvements.