Along with the life sciences and physics, marine science is one of the few fields where major new discoveries are likely in our lifetime. 70% of the earth's surface is covered in ocean, and frankly we don't know all that much about it. This is especially true about the deepest parts and how human activities will end up affecting marine life in the coming decades.
Also like biology and physics, marine science has plenty of useful real-world applications, especially in terms of conservation and resource extraction. Unlike in those other disciplines, however, marine scientists are expected to be generalists. Geology, oceanography, chemistry, mathematics, physics, ecology, and biology are all covered at an undergraduate level. Even if you later choose not to work in marine science as such, a broad knowledge of science is an incredibly useful thing to have.
Typical undergraduate specializations include aquaculture, marine biology, biological or physical oceanography, and coastal resource management. A good balance of academic study, lab practice, and fieldwork is maintained. In many cases, it's also desirable to spend as much as a year studying abroad to gain first-hand experience of different marine ecosystems.
The most successful students are often those with the ability to synthesize knowledge. In other words, it's great if you can interpret large amounts of raw data and draw conclusions based on your knowledge of several different sciences. Attention to detail, an interest in environmental issues, and a willingness to get your hands dirty will also stand you in good stead.