0/1 Knapsack - State Design

What information do you need to make a decision about item $i$? You need to know which items you've already considered and how much capacity remains. Define $dp[i][w]$ as the maximum value using items $1$ to $i$ with capacity $w$. Here $i$ ranges from $0$ to $n$, and $w$ ranges from $0$ to $W$.

This gives you $(n+1) \times (W+1)$ states. Each state ($a$ specific combination of $i$ and $w$) represents a smaller problem to solve: "What's the best I can do with these items and this capacity?"