The pseudocode
For each production RA → RB RC:
if P[j,k,B] and P[j+k,i-k,C] then set P[j,i,A] = true
Should be interpreted in the following way. Suppose that it's the case that P[j, k, B] is true. That means that the string formed from k characters starting at position j can derived from the nonterminal RB. If it's also the case that P[j + k, i - k, C] is true, then the string formed from the i - k characters starting at position j + k can be derived from nonterminal RC. Therefore, since RA → RB RC is a production, it's the case that the string formed from the i characters starting at position j can be derived from RA.
I think it might help to interpret that pseudocode as
For each production RA → RB RC:
if P[j,k,B] == true and P[j+k,i-k,C] == true, then set P[j,i,A] = true
Hope this helps!