Free-form role-play is, for the most part, multiple people getting together and creating a story by "playing" as characters. It can be structured or loose, it can have a goal, or just let things happen. The beauty of free-form RP is that it's free. There are no rules except those the players set for themselves. There are no scores or experience points unless the players involved want them. Everything is up to the players.
Though the reasons and motivations for FFRP can vary greatly, a few seem nearly universal. A reason most participate in FFRP is because it allows them to act out things they would not be able or wish to do in real life. It could be something fantastic, like training to become a wizard, falling in love with an extra-terrestrial, or playing an honest politician. It can be something mundane, like going on a blind date, or making one's way up the corporate hierarchy. Whatever the reason, it allows people to be someone else. (Or, in some cases, be their true selves.)