Think for a second about hydrofluoric acid. You've probably heard it's reputation as one of the few things that can dissolve glass, right? It's very dangerous, and can do things others can't, but it's actually classified as a weak acid. You probably already learned this, but in case you didn't, I'll say it.
an acid, going by the Bronsted Lowry definition, is any compound that can give away a proton (H+) to a solution.
A Bronsted Lowry base, is any compound that will accept a proton (H+).
A strong acid, is a compound that can easily and efficiently donate it's protons to a solution.
A weak acid, is a compound that does not donate these protons as efficiently.
To give an example, HCl easily disassociates in water. It easily separates into H+ and Cl-. Now, say you have a bunch of HCl molecules. A pretty good percentage of them will separate, while maybe a rare few will stick together. HF (Hydrofluoric acid) is a little bit different. It is classified as a weak acid, because when it separates into solution, giving H+ and F-, that F- anion will attract the H+ back to it. So if you drop HF into water, some of it will separate into H+ and F-, but a percentage of that will attract back to the F- anion, and stay there.
Now, say you have a way to deliver that F- anion, without losing any H+ cations to the solution. It would still want to attract a H+ from somewhere. Water, being a protic solvent, would donate one of the H+ cations from it's structure, forming stable HF, that won't disassociate, and -OH anions floating around in solution. The acceptance of this H+ by the F- classifies the F- as a Bronsted Lowry base.
Now, how do we get this F- anion into that solution? What could we possibly use to carry it? How about everyone's favorite lavender burning alkyl metal friend? It turns out, Potassium (K, or K+ in this case), is a perfect vessel for delivering this F- anion, because the F- anion has little interest in sticking with that K+ cation. So, more H+ cations would be absorbed by the F- than K+ anions would, thus making it a Bronsted Lowry base.
As for the KCH3COO3, I don't even know what the hell that is. I don't even think it exists to be honest. Next time you see your teacher, ask him to draw a lewis structure of it, and if you can, post a picture of the structure, please, because it's really got me stumped. If I had to guess though, the K leads me to believe it's a base.
Eh, hope that helped, and if I was at all inaccurate about anything, it would be appreciated for the higher nerds to correct me.