It depends. If the state you are talking about is your resident state, your full-year resident state does tax all of your income. However, if the state in question is either a part-year or a nonresident state, there is another explanation.
In many states, part-year and nonresidents are taxed as follows: The state calculates the tax based on the hypothetical of what would be the tax on all of your income, and then prorates that amount of tax to the percentage of income actually earned in the state to determine your actual tax. Let's say, for example, that you earned 20,000 in the state in question, but 50,000 overall. Let's say that you would pay 2,000 of tax on 50,000 of income in that state. Your state tax would be 800, which is 40% of the hypothetical tax, because 40% of your income came from that state.
Thus, all of your income would be factored in to determine the state tax, but income not taxable in the state is not actually taxed there.