What are some examples of sequential-decision tasks?
One kind of sequential problem is making control decisions in real time. Consider the problem of driving a vehicle. The system will have a state, you can observe some measurements, and you must make a decision. You decision generates and input which then affect the future state of the vehicle and the whole process repeats. A problem which interacts with an external entity that changes its behavior based on a decision is sequential in nature. Other examples include things like optimally managing a stock portfolio, searching for an evading opponent, optimally playing a card game. 

One non-sequential problem is classifying the fruit on a scanner in a grocery store. A measurement is taken, the data is processed and and output is determined. When the output generated does not alter the nature of of future outputs, it is non-sequential.