Your brakes are not fine if the ABS light is on. ABS stands for Anti-lock Braking System and is the system that keeps your wheels from locking up under hard braking conditions. The only time you would see the effects of the ABS system is when you slam on the brakes; at that point if they're pressed hard enough to lock them, then you'll feel a shuddering in the pedal that indicates the ABS system is releasing the brake pressure momentarily to let the wheel turn slightly so it's not locked and skidding.
The upshot here is that your brakes are indeed working normally under normal driving conditions, but will not help you out should you slam them on and go into a skid. Here in the US, ABS has only been required on cars since 2013 although Europe mandated it in 2004. So yes, you can continue driving it without fixing the ABS, but you'll be doing without an important safety feature that could save your life.
Generally the most common cause of an ABS light is that one of the four wheel speed sensors has failed or become disconnected. It is possible to test them yourself, but a shop can hook the car up to a scanner and determine exactly why the ABS light is on, which could save you time and money if you know what to replace or fix rather than just guessing.