You have either stretched the cable(s) or pulled them out of alignment, both of which can usually be solved by re-adjusting them.
The adjuster can be found at the point the cables reach the lever, but depending on the design it may be inside the car (under some trim between the seats) or underneath - Your workshop manual should tell you which it is, and how far to adjust it. Generally you should aim for it to be fully engaged 3-4 clicks before the top of the lever's travel, but that does vary.
One caveat is that if the cable has stretched too far, there will not be enough adjustment left to tighten it, in which case you will need new cables. Replacement is obviously a more complicated job than adjustment, but usually still within the scope of a fairly competant DIY mechanic.
The danger of driving a car with a non-functional handbrake is that you no longer have an emergency brake in the event of a service brake failure. Additionally, you won't be able to park on a slope! (unless it is a manual car and you park it in gear)