Here's my understanding:
1) Pka and Ka are inversely related, so a higher Pka means a smaller Ka, and vice versa
2) Since Ka is a product to reactant ratio, a higher Ka means more product formed, which means a stronger acid
3) Once and acid-base reaction has finished proceeding either forward or backwards, it has reached equilibrium
4) An acid will form a conjugate base, and a base will form a conjugate acid
5) The stronger an acid, the weaker a conjugate base. Why?
Simply because a stronger acid will dissolve to almost 100% (let's say for the sake of the explanation, to 99.999%). That means that we now have 0.001% acid left for 99.999% base in the reaction, at equilibrium. Therefore, the 0.001% strong acid is counter-balanced by 99.999% weak base,k so the base has to be very weak, otherwise due to the much larger quantity, we wouldn't have an equilibrium