Somewhat recently, the topic of trainer to student relationships came up on tumblr, and since we're equestrians there was a strong amount of disagreement. In reality, everyone is different. Some people may never talk to their trainer about anything except riding while others may be their trainer's best friend (though I personally advise against this). I'm more of an in between type, and while I lean towards the "best friend" end of the spectrum, I do intend on staying closer to center.
Regardless of your comfort level with your trainer, I find that an importance must be placed on how you communicate with them. It's easy to nod your head and say "Yes" when your trainer asks if you can feel your horse doing something, and I am guilty of doing this, but it does you no good. If you're confused, ask questions. Never be afraid to ask questions. You're likely to get some more knowledge along with your answer.
A situation that I've heard about quite often (and have been in) is where a student has been assigned to a horse that they either don't feel comfortable on or are consistently struggling to the point where progress is stunted. For the most part, trainers have a reason for putting you on a certain horse, and you should trust their judgement, but if you start resenting riding because of it, tell them directly. Discomfort won't always show up in your riding; my telltale signs of nervousness disappeared after a while despite me still having regular losses of confidence. Be straightforward, and don't let it escalate. This goes for ANY concerns you have.
Related to the last point is being able to communicate your goals to your trainer. Helping you achieve your goals is part of a trainer's job, but they can't help you unless they know what those goals are. Want to find a move up horse? Tell your trainer, they might know of a few. Looking to educate yourself on barefoot trimming? Your trainer could offer some good reads. Your trainer likely has goals and hopes for you too, and it's their job to let you know what those are, especially if they're time sensitive.
Being able to communicate your questions, concerns, and aspirations to your trainer goes a long way in helping you develop as a rider and horseperson. You are under no obligation to tell them your heart and soul, but the job of a trainer is to train you to be your best, and that cannot happen without some openness between you two.