The main reason was to give Poland a major sized seaport. Much of what is modern day Poland was at the time, still part of the German Empire, due to the historical impact of an expansionary Prussia from the 19th century. Whilst many lands were stripped from Germany following WWI, many areas that they wanted to remove were German in terms of population and culture, which made it more difficult. Danzig was supposedly about 95% German in 1920. Therefore, it was felt putting thousands of Germans into a new Polish state may not be the best idea. However, Poland and its supporters still wanted it to have that seaport, for economic and political reasons (easier to be more independent from Germany trade etc). Thus, a free city was created as essentially a bit of a fudge, to give Poland what they wanted, but not push a wholly German area over into being actually part of Poland.

It should be noted that whilst the city was not part of Germany or Poland, it was also not an independent state. It was put into a customs union with Poland, plus, Poland had control (and the right to maintain) all infrastructure, so it was actually, in many ways, Polish, but NOT in name - and that was what was important.

Source/More info: http://bigthink.com/strange-maps/42-the-free-city-of-danzig-1919-1939