When witnesses come to Jerusalem to testify that they have seen the new moon, the judges interview them in order to ascertain that they have, in fact, seen the beginning of a new lunar cycle (which looks like this) and not just the end of the previous one (which looks like this). These shapes are what the moon looks like in Israel at the beginning and end of each lunar month. The closer one gets to the equator, the flatter the crescent of the moon becomes, until it can look like this.
Someone who does not pay close attention to the position of the moon may very well walk into court and describe a situation that is physically impossible. To assist the witnesses in their testimony, the Mishnah on our daf (=page) tells of models that Rabban Gamliel had in his study, which he would show to the people coming to testify. In this way, situations that might be difficult to describe verbally could be discussed with the help of visual aids.
(For a series of multimedia presentations on the moon and lunar months, see http://www.daat.ac.il/daat/shabat/luach/month3.html.)
The Gemara questions how Rabban Gamliel was allowed to fashion these devices, when the baraita interprets the passage (Shemot 20:20) that forbids the creation of idols and graven images to refer specifically to heavenly objects like the sun, moon, stars and constellations. The answer offered by the Gemara is a difficult one – that Rabban Gamliel did not make the models himself; they were made by others. Tosafot and other rishonim argue that it is forbidden for Jews to have non-Jews perform tasks for them that are Biblically forbidden, which would seem to be the case here. A number of explanations are offered:
Most commentaries suggest that, since this was done for an essential reason connected to fulfilling a mitzvah, it was permitted in this case.
The Ritva suggests that others made the models for their own purposes, and Rabban Gamliel purchased them from those people.