It is used to mean that if you do a small favor for someone, they will become greedy and ask you to do bigger and bigger favors for them, making you regret doing the first favor.

e.g., Be tough and uncompromising – if you give colleagues an inch, they will take a mile.

I told her she could borrow the car for one day, but and she’s been 

gone a week. She always does this, you give an inch, and she’ll they’ll take a mile.

Tradução: Dê a mão e ele/ela vai querer o braço.