I don't have time to answer this fully right now, but basically the East India Company initially got to have administration over parts of India because they were granted a diwani by the Mughal Emperor, the ruler who officially controlled much of the continent. If you have a diwani, you can collect taxes and revenue over the area you're the diwan of, for yourself and for tribute for the emperor, but you also have to administrate it. They got the area that pretty much corresponds to Bangladesh and some extra land to the west and south which are part of multiple states within India today. I don't know how profitable the overall company itself was, though initially it was very successful, but many British people made personal fortunes by working in India, and corruption was definitely an issue. People also generally profited off of spices, textiles, and crops like coffee, tea, opium, and indigo. (Some of those didn't come into greater focus/prominence until after company rule was over though.)

The East India Company even had its own private army dedicated to protecting its trade interests. Various local powers, the British, and the French were all vying for control of places and making different alliances to further their own profit and power. The British ended up effectively kicking the French out of India and acquiring a lot of land in various treaties, in additional to the area they were given a diwan over.

So it wasn't that they wanted to have control over new places just for the sake of it. It came with the circumstance, and became very important for securing company and later colonial interests, since making laws lets you further whatever outcome you want to see. You can control taxes, oversee production of whatever crops and materials you want to further your own interests, make laws so that you can ensure your place of power will stay as it is for a long time, ect...

(Fun fact: one reason the British started growing tea in India was because a pathogenic fungus was destroying their coffee plantations in South India and Sri Lanka. They had this whole campaign to get British people to switch over to tea instead of coffee, which in itself was pretty successful in the 19th century.)

More info:

A Concise History of Modern India - Metcalf & Metcalf

Corporate Governance in India - Das

Nabobs: Empire and Identity in Eighteen-Century Britain - Nechtman

The coffee reference is from Global Tea Breeding: Achievements, Challenges and Perspectives - Chen.

Edit: fixed my English