Physical contact with the arm is typically a part of flirting. It is testing the waters by one person to see if being in the other's personal space feels right. The arm is probably the least offensive place on the body to touch.

Physical contact is a pivotal moment in getting to know one another. Before this point of touch, a boy and a girl try to decide if they like each other: Do I find her cute? Does he like the same kind of music I do? Does she feel genuine? Do I like his snarky humor? Afterward, assuming both are okay with the contact, they start to consider how much they like each other: Is he fun when hanging out? Will she play tennis with me? Can I trust him with my secrets? Do I want to make out with her? Should I ask him to go steady? Should I move with her to Hawaii?

When the touch happens, it is usually brief and may seem accidental or incidental. If the touchee flinches or retreats, this means "not going there" (or "Aaugh! Cooties!") or at least "not ready yet." If the touchee doesn't retreat, this means the contact is welcome, or at least tolerable. Contrast this to when one person bumps another in a crowd, the brief exchange ("sorry.", "excuse me", "watch where you're going, doofus!" etc.) is to assure "hey, I touched you by accident, and didn't mean anything by it."

In past eras, it would be the boy's role to initiate conversation, and then the girl would, when she felt ready, make that first touch. Nowadays, gender roles are more fluid, so either person can initiate conversation or make the touch.†

Regarding the incident that sparked this question, it is most likely the boy was being a tad forward. The proper (contemporary‡) response to this is to let him know you don't want to be touched (yet), and then he should respect your personal space. Or, if you do want him in your space, don't back away, let him hang, and see where things go.

Further Notes:

* Physical contact in tight crowds (i.e. tightly packed busses or streetcars) is much more likely about the lack of room than a come-on. Still, noone should be groping you where you don't want. * We all learn through trial and error. Assume he (or she) is being clueless unless you're pretty sure he's intentionally being a jerk. * It's okay to change your mind, or express a limit at any point and expect it to be honored. This is no matter how hot and heavy things get. * It's also okay (sometimes preferred) to make or indicate adjustments rather than merely retreating if, say, you want him to hold you at the waist and not at the arm, or you want him to grope you some places and not others. * If he's unresponsive to subtle cues, get verbal (i.e. "Don't touch me.", "Back off." "That hurts." "Leave me alone."). If that doesn't work, it's time to defend yourself physically and/or inform the authorities. Unwelcome touch is assault and needs to be treated as such. † So far, we've assumed a heterosexual pair open to romantic intentions, though this process occurs between LGBT persons, or individuals establishing a platonic relationship. In formal platonic relationships the cordial greeting and handshake serve as a ceremonial version of this process.

‡ In earlier, less enlightened times, the girl was alwaysexpected to coyly reject the boy, and he would then begin a process of wooing her affections, on the basis that she would eventually yield to his advances. (Note the girl has no actual say in this model of romance.) It is from this that all the if she says no, she means yes beliefs were retained. In contemporary times, you can assume safely that if she (or if he) says "no" she means it. Go ahead and walk away. If she meant "yes" she'll seek you out, and not be so quick to reject you.