The ways your body, or a piece of metal, or any thing else with magnetic or electrical properties different from air can interact with an antenna are complex and numerous. Let's take your example, you moved your hand around an antenna, and the reception got better. Why could this be?
Your body is reasonably conductive, especially to high-frequency current. By placing anything conductive near the antenna, it becomes part of the antenna through mutual inductance and capacitance.
The new antenna (the antenna proper + your body) has different characteristics which may be better or worse than the antenna proper alone. It will likely have a different radiation pattern than before, which may be more sensitive in the direction of the signal, or less sensitive in the direction of noise. Either will improve the signal-to-noise ratio, which is the limiting factor in most wireless communications.
Your body can also absorb, reflect, and refract radio waves. Multipath interference can be a problem for wireless communications. By putting your body in the path somewhere, you may eliminate one mode of propagation which was interfering destructively. Or, you may enable a mode which will interfere constructively. Thus, you make the signal better or worse.
Small devices tend to have smaller than optimally sized antennas. Your body, some part of it, or something else might be a more efficient antenna than the device's antenna, and by coupling to it (again, through mutual capacitance and inductance) you might make a more efficient antenna overall. Of course it's just as possible that you make a less efficient antenna.
If you want to predict what body positions or materials might improve the signal, that's hard. You could solve Maxwell's equations, taking into account the electrical properties and geometry of everything between and near the transmitting and receiving devices. Of course, that's absurdly hard.
The reason it's so easy to improve reception by waving your hand on or near an antenna is that you can very quickly try a lot (you might say infinitely many) possibilities, and if you can get some immediate feedback on what's working (by listening to the signal, for example), your brain quite naturally finds the optimal configuration.
As for what materials besides your body might work, just about anything conductive will do something. Your body works well because it's quite large and easy to control accurately. Waving something conductive around your antenna, you can probably find a configuration that works better in a particular position, receiving a particular station, at a particular time.
If you want to find some material or technique that consistently or universally improves reception, that's called antenna design. For example, a Yagi-Uda antenna has some pieces of metal of a particular size in a particular geometry which consistently make the antenna directional, being less sensitive in some directions and more sensitive in others. If you point it at the station you want to receive, it works better than a non-directional antenna almost always.