You are nearsighted and have astigmatism. O.D. is your right eye, O.S. is your left eye. Sphere is the correction for nearsightedness and cylinder corrects for astigmatism.
Astigmatism is an irregular curvature of the eye--its less round and shaped more like a football (its very common). Astigmatism causes you to see things somewhat distorted. You know that weird curving you get in new glasses--that is the correction for astigmatism. You see walls as curved but your brain nows that's not possible so it tries to straighten it out for you. Then when you get glasses to correct for astigmatism your brain is still compensating and you see that curved affect until your eyes adjust to the correction. Axis is the degree of your astigmatism is set at (180 is the highest).
And yes your eyes are somewhat bad. Sorry. Anything above a -3.00 in sphere is starting to get up there. And anything above a -1.00 is considered high for astigmatism.
To make things simpler when referring to your prescription you would add the sphere and cylinder powers together to get what is known as total power. Total power for your right eye is -5.50 and your left is -5.75. you can just round off even further and just say you total power is about -5.50 when talking about your prescription.
One more thing, you would say your prescription its "minus five fifty, total power" rather than "negative five point fifty." (positive and negative is for math not optics)
But while your prescription is a bit up there, it isn't until minus 8 or 9 or higher that its considered really bad. Prescriptions of minus 15 or 20 are very rare.