Hello,
The carbonic acid/bicarbonate buffer system is so exciting because it's so important for your blood! Without it, your pH could change to a point where your enzymes don't function and you die from your own body's toxicity.
But that's besides the point, it's just exciting when what you learn in chem has a connection to something important in life =P
To answer your question, if you've learnt about buffer systems, you'll know that they involve a weak acid and it's conjugate base. You would have also learnt Le Chatelier's principle by now (a system in dynamic equilibrium, which is disturbed would shift to the side which would most minimise the disturbance). Thus, when we have the equilibrium of the weak acid and it's conjugate base (in this case, H2CO3 and HCO3), the decrease in pH (high conc. of Hydrogen protons) would cause the equilibrium to shift to the left, making more H2CO3, decreasing the amount of H+ and thus decreasing the acidity. If there is an increase in pH (low conc. of H+), the equilibrium would shift to the right to make more H+ ions, again minimising the disturbance and balancing the pH once again.
When it comes to blood, the increase in acidity would be caused by CO2 gas bonding with the water in your blood to form H2CO3. Too much of CO2 will make your blood acidic, which is why getting rid of carbon dioxide in your body is so important!
You might do an experiment with acetyl acid and it's conjugate base, adding acid and base to it. You'll see that the pH would hardly change compared to when you add the acid or base to other solutions. Which is really cool!
Remember, though, that the buffer system is not infinite, as in if you add HEAPS of acid/base, it wouldn't stabilise it. The large amount would be out of it's capacity and there would be a larger increase/decrease in pH.
Hope it helps!