Determination of the Acid Dissociation Constant?

You're not providing all the info.

(1) You calibrate the pH-meter  because you want its reading to represent accurately the true pH-value. When you calibrate against 2 buffers you ensure that you have increased accuracy for measurments that fall within the range set by the two buffers.
Acetic acid is a weak acid. Thus for a moderate concentration we expect the pH to be within the range 4-7 (acidic but not extremely acid). So you use buffers for that range.

(2) Acetate is the conjugate base of acetic acid. When you add base to an acid you increase the pH of the solution. You should note here that you will be forming a buffering system, so as you keep adding sodium acetate, at some point the increase in pH will be smaller and smaller (it will be minimum at pH=pKa=4.75) and then once you pass the optimal buffering range (conc. acetate >100*conc acetic acid) the pH will increase faster until you approximate the pH value that you would expect if you had only acetate -I don't know what concenration that would be since I don't know that of the acid but given that pKa=4.75, that maximum pH value can't be really higher than pH=9.5 no matter how much acetate you add.
OR if you are looking for a simpler explanation for lower level chemistry, according to Le Chatelier's principle the equilibrium CH3COOH <=> CH3COO- + H+ will be shifted to the left when you add CH3COO- . This means that the [H+] will decrease and pH will increase.