Freestyle is a roleplaying system "without rules"--that is, without all the dice rolls and number formulas that accompany systems such as D&D. While other systems use randomly generated numbers to produce balance to a story, freestyle relies on skillful communication and common goodwill.
This system works best when used collaboratively between RPers who know each other well and have similar ideas of what to expect from a game. When everyone understands that, say, players do not kill other player's characters and that PCs do not blow up countries, players are not going to kill other player's characters and PCs are not going to blow up countries. Furthermore, the players are not going to argue angrily with each other about why it should or shouldn't be done.
The downfalls of freestyle become most apparent when RPers have different ideas of what an RP should be. If one player believes character death is acceptable, and kills the character of another player who disagrees, bad feelings are going to develop quickly--especially if the two players cannot come to agree, out of the game, about character death.
These sort of problems are the exception and not the rule, however. Freestyle remains the system of choice for most minor, spur-of-the-moment and unplotted RPs. Few dramatic or irreversible problems arise during freestyle RPs.