This means exactly what it says, but during meditation takes on a much more complex meaning. We go through life each day pretty much knowing the boundaries of what will happen. If a stranger were to walk up to us we internally assume they want directions or have a general question for us. We go to the store, choose our goods, go through the check out and most of the things we got are generally predictable. We all take these things for granted, and when something happens outside of that predictability we generally do not like it. Often it is associated with undesirable effects to us.
When you meditate, whether you know it or not, you unconsciously setup expectations or conditions. This starts off simple enough. You expect to relax, you expect to release tension from your muscles or core, you expect to find some relief from your day-to-day concerns etc. These expectations, although they may be subconscious and we aren't aware of them, they are there and often feed the babbler. More so, they greatly limit the depth of meditation you will experience. For the novice, it can make the difference of finding yourself frustrated half way through your meditation because you are dissatisfied that you are not relaxing as much as you had hoped or expected. So by default your session has ended or ironically created more frustration and self-disappointment.
For the more seasoned practitioner, it is the difference of sitting in quiet solitude and never experiencing a divine moment, or "spiritual moment" with the universe or God. Those who understand that expectation creates limits within them or defines what they may or may not experience often become the mystic themselves. It's hard to define what God shouldn't or should be; it just as hard to know what absolute inner peace will be like if you are trying to find it.
Non-expectation means that there is no such thing as a bad meditation. It means if you have not set an expectation then you leave self-judgment at the door and can really relax. It means if the universe decides to present itself to you it won't avoid you in fear that it may disappoint you.