If a farmer wants to increase the health of his crops, he could apply a nitrogen-based fertilizer. why is nitrogen important to plants?

Not only for plants, but also for every organism and every life form nitrogen is important because it poses as catalyst that supports different is chemical reactions of growth. N is filled with chlorophyll that actually gives you the answer on the question as chlorophyll allow plant to perform photosynthesis by absorbing energy from light that leads to the growth. So, it is important because it provides photosynthesis.