Trends is a simple graphing system for search volume. You can filter trend searches by geographical area, but that's about it.

Insights is a quite-a-bit-more-in-depth version of trends.
It'll give you sub-category searches,
It'll allow you to search within specific time periods,
It'll allow you to filter various searches (video, image, web, etc.),
It'll try to predict trends over the next month (forecast),
It'll allow you to search and filter trends categorically.

orvn has some great points and is right on the money but in general you should always get your information about Google straight from Google's sites. They've got tons of help articles, guides and tutorials if you just look around. You might not get someone as knowledgeable as orvn to answer your questions in the future.

Once you've got all the information you can get from Google and have specific questions or comments about what you now know this is a great place to bring them. Also make sure that your exact questions/comments have not already been voiced.

Not trying to single you out specifically, its just that I haven't even been here that long and I'm already seeing the same type of broad questions every single day. If you stick to the methodology I mentioned above you'll have a solid foundation for all your SEM efforts.

Anyways, you'd use trends to get the feel of a niche and once you've got a niche you like you can focus your gaze using insights.