The phrase "to keep up with" means to maintain pace or progress in line with something else. It can refer to trying to match someone's speed, level of productivity, development, or advancement. For example, if you are trying to keep up with the latest technology trends, it means that you are making an effort to stay informed and adapt to new developments as they happen. Similarly, if a company is trying to keep up with demand for its products, it means that it's working hard to produce enough goods to meet consumer needs. Overall, "to keep up with" implies a sense of striving to match or surpass something else in order to succeed.