If someone asks to follow you, you will get an alert in your Inbox like this.
If you accept the connection, that person can share content with you (Hey, take a look at...)
They will also get access to any of your profile information that you make available to "friends." See Who can see what about me? for more on your privacy settings in your profile.
Obviously if you reject or ignore, then that person will not be considered your "friend" for privacy purposes, and will not be able to share content with you.