Servile describes someone who is almost aggressively helpful, like a teacher’s pet who insists on bringing an apple every day even though the teacher doesn’t want it. To call someone servile is an insult.
To remember servile, think of the word servant — they both derive from the Latin servus, "enslaved person." The Servile Wars, for example, refer to slave revolts in the Roman Empire. These days, servile describes someone who is so eager to please that it makes you cringe. If you apologize when someone else steps on your foot, you’re being servile.