We know that carrying things on Shabbat is not permitted if we are carrying them from the home (private domain) to the street (public domain). What about throwing? - This is also prohibited. In effect, one uproots from the home and lands it in the street, so it has the two elements of the transgression.
What if he hands an object over or throws it from one home to another, with the public street in between? Here, Rabbi Akiva makes him liable, while the other Sages do not. What is the argument about? Rabbi Akiva says that there is another principle: an object flying in the street is as if resting there. Thus, we view it as if having landed in the street. The Sages do not agree with this principle.
But why is handing over forbidden at all? All kinds of labor needed for constructing the Temple is what is forbidden on Shabbat. And why? Because the Temple is the microcosm of Creation. Since in building the Temple in the desert the Levites were handling beams from one wagon to another, this labor is forbidden.