"Always do right." - This means always do the right thing, be a good person, and always do good works. "This will gratify some people"- By doing good things, often you will do good things for someone else. This will gratify that person. That is, they will be happy that you did something good for them. "And astonish the rest" - If you never do something bad, that would be very amazing. Everyone would be "astonished" that you are always able to do good and help people.

It means, when you always (try to) do the right thing, some (few) people who also believe in doing the right thing will be pleased with you, while the rest (most people), who don't believe in doing right, will be surprised by you. (And may criticize you, for doing something they didn't consider worth the effort, etc...)