If checked, the "Remember Me" checkbox on Blogger's home page will automatically log your account into Blogger when you return in the future.
This is a good idea if you're the only person using the computer.
It is a bad idea if it is a publicly accessible computer, or if you're sharing the computer with other folks.
Notes:
- Occasionally Blogger might seem to forget that you've checked the "Remember Me" checkbox- this is because the cookie that remembers your account information is set to expire after 2 weeks. If this happens to you, log in again with your Blogger username and password (and check the box if you wish).