State of variables in dynammic programming I would like to know  what a state variable is in simple words, and I need to give a lecture about it.

I have chosen the Longest Common Subsequence problem
I found a similar question but it has no answers. I was told that I need to use the "states of variables" (not sure if variable of a state and state variable are the same) when explaining the pseudocode. 

I think it has something to do with Hoare logic and state variables but I'm a very confused.

If you can provide useful links or maybe a clear explanation would be great.
Dynamic programming was
invented/discovered by Richard Bellman as an optimization technique.
The notion of state comes from Bellman's original presentation of
Dynamic Programming (DP) as an optimization technique. This is
presented for example in the Bellman equation entry of Wikipedia.

The technique was then extended to a variety of problems.

You might usefully read the Wikipedia presentation, I think. The
concepts you are interested in, including that of states and state variables, are described there. It may still be
some work to see how it fits the algorithm you have to explain.