The domain name and the whole URL of a site tell a lot about it. The presumption is that if your site is about dogs, you will have “dog”, “dogs”, or “puppy” as part of your domain name. For instance, if your site is mainly about adopting dogs, it is much better to name your dog site “dog-adopt.net” than “animal-care.org”, for example, because in the first case you have two major keywords in the URL, while in the second one you have no more than one potential minor keyword.

When hunting for keyword rich domain names, don't get greedy. While from a SEO point of view it is better to have 5 keywords in the URL, just imagine how long and difficult to memorize the URL will be. So you need to strike a balance between the keywords in the URL and site usability, which says that more than 3 words in the URL is a way too much.
Probably you will not be able to come on your own with tons of good suggestions. Additionally, even if you manage to think of a couple of good domain names, they might be already taken. In such cases tools like the Tool below can come very handy.