Everyone carries his own expectations to a shoot. After my time assisting, I realized that my expectations did not always match up to those of the photographer. This can create friction, so it's important to recognize what sort of assistant the photographer is after. For the record, I had no problem doing my damnedest to fulfill any of these roles in any combination. Except flunky. I can't do flunky, apparently.
Laborer Almost always, whatever else the photographer wants, he wants a laborer to some degree, whether it's hustling equipment from the van to the location, setting up grip, or moving "that flag, no not that one, just a little...no the other way". But sometimes, that's all he wants - he doesn't want advice, or conversation, or to have to answer questions about his career.
Flunky Sometimes it happens that the photographer doesn't need a photo assistant at all, and he just wants someone to make him look good, whether that's by clowning around, nodding excitedly at everything he says, or being the butt of his jokes all day.
Consultant This is what, ironically, it seems most new photo assistants want most to be, for good reason; but youth is wasted on the young. When the photographer wants this, and you're ready for it, it can be superb experience, and a superb experience - she tells you what she's after, you make a suggestion or two, she picks one and perhaps offers some modifications, and you execute it together.
Producer Provided there isn't already a producer, and there are enough assistants, any good assistant should be able to coordinate all the minutiae of a shoot, whether that's coordinating models, picking and arranging for gear, managing other crew members, or even keeping the photographer on schedule. This is probably the most dangerous thing to misjudge though, because if someone else thought he was doing it, and you come in all "oh no I got this", it'll result in hurt feelings at best.
Protege While this can look an awful lot like Flunky, it's fundamentally different. The photographer needs to pass along some of her experience, and while this is often true incrementally, sometimes it happens that it becomes the primary thing, and you end up behind the camera much more than usual, or getting an eyeful of the bidding process. Be grateful for times like this.
Windowdressing I doubt anyone will ever want this from me, but I have seen it: an assistant who is primarily someone nice to be around. Attractive, personable, charming, and almost no assisting skills.
Therapist Sometimes the photographer needs a lot of moral support, and might look to you to provide it. Depending on the personality of the photographer, this can be a really gratifying two-way street of exploration and discovery, or it can be a hellish crawl down a dead end lane. It's not like you really have a choice though - if they're going to lean on you, you can't just let them fall over.
PA Oh you thought you were going to be handling lights, maybe triggering the camera for a couple test shots? Ok, but can you go to Starbucks again, first? And then we need you to go to Brickley and get another EZ UP, this one's blue.