To ignore something is to disregard it. If you ignore the rules of grammar, you're likely to be misunderstood.
It's easy to see the relationship between ignore and a word such as ignorant. To be ignorant of something is to know nothing about it. A good way to be ignorant about something is to ignore it. In other words, if you want to be ignorant about a certain subject—that is, if you want to know nothing about it—then by all means ignore it. Pay it no mind.