This phrase means to like an idea. It's usually used to talk about an action that people are debating on. For example, if people in the government are discussing whether to raise or lower taxes, you could say:

I'm strongly in support of the idea of raising taxes if it means improving our education system.

The phrase "in support of" is not really casual or formal, but it's usually used to talk about decisions so it's likely to be used in politics, classroom discussions, and in the news.