Previous Transformation: Enchantix
Next Transformation: Harmonix
Believix is the new transformation the Winx get in Season 4. It is the transformation after Enchantix, but due to the fact the girls fly back to Magix at the end of the season, it is said not to be the final form, and as Miss Faragonda said in the first episode of Season 4, Believix is a higher level fairy form which can be accessed by Enchantix Fairies, but it was never mentioned by her that it was the Final Fairy Form, but only one of many other Higher Level Fairy Forms.
For a Fairy to earn her Believix form, she has to make people believe in fairies and magic, thus Believix can only be earned on Earth or somewhere where people do not believe in magic. Believix gets stronger when more people believe in magic, which means that if a fairy does not convince people to believe in fairies and magic, her powers will weaken.
The Winx Club earn their Believix in Season 4 episode 6 because Roxy believes in them. Roxy also earns her Believix in Season 4 episode 12 but in an incomplete way - using her will to transformation. It is Roxy's first transformation, without earning her Winx, Charmix and Enchantix before.  In Episode 4x19 the Winx earn another new power called Sophix, this is one of the Gifts of Destiny (the Gift of Wisdom) and give the Winx flower and plant powers akin to Flora's and the ability to be in complete harmony with nature. The Second Gift (the Gift of Heart) boosts their courage and they earn Lovix, a transformation that gives them ice powers. The Third Gift (the Gift of Darkness) did not give the girls a new transformation, it was instead a power to bring someone dead back to life, but they could use it only one time.
A question arose when Stella first appeared in episode 1 of Season 1. She got Bloom and her family to believe in magic but did not earn her Believix. This is most logically explained that a fairy must have her Enchantix to earn her complete Believix. Miss Faragonda herself confirmed it by saying that it is a Higher Fairy Form accessible to Fairies who have already gained their Final Fairy Form, their Enchantix.
With Believix, a fairy has the power to reach out to someone's heart and help people overcome their bad habits or weaknesses. Every fairy has a different type of this power:
Gifts of Destiny
The powers of Believix Fairies are ineffective against Major Fairies of Earth as these are the Supreme Guardians of Nature, and of Earth's magic. Therefore the Winx needed higher powers to face the Major Fairies and were given the Gifts of Destiny by the Ethereal Fairies. The Gifts of Nature provide Believix Fairies with two more sub-transformations: Sophix, that allows them to unite with nature in the Kingdom of Diana, and Lovix that halps them in the cold regions of the North were Aurora rules.
Gallery of Attacks
Every girl has a special effect added to their attacks, which is different for every girl and has something to do with their main power.
Gallery of Believix Powers
When the Winx girls first arrived to Earth, Miss Faragonda told them that the final fairy form is Enchantix, but that there are many other, higher, levels of transformation with powers which are different than those of Enchantix, and are gained in specific situations, in the case of Believix it is by making people who do not believe in magic start believing in it, and that the fairies can then use these powers instead of their Enchantix powers. This would probably mean that the normal final fairy form is effectively Enchantix, and that Believix is in fact a higher level transformation, above the normal fairy levels, and that the fairies who have accessed Believix level have the option of using either Enchantix or Believix or any other higher fairy level (Faragonda said that there were many others) as they wish, which explains why the girls used Believix instead of Enchantix in the second movie.
Something else which suggests that Enchantix is the final form is that students at Alfea undergo a three-year course, the first one to control their standard fairy forms (their Winx in the 4KIDS version), the second one to earn their Charmix, and the third one to get their Enchantix. Believix is not studied at Alfea, as it is not a normal fairy level, and not anyone can earn Believix powers (so far in the series almost the whole Universe, Earth included after season 4, believes in magic, and therefore it is very difficult, to earn Believix anymore, although there are likely people on some other planets who refuse to believe in magic or doesn't have their magic at all). These higher level transformations are mostly supposed to be magical evolutions from Enchantix, which remains the base transformation from which these powers can be accessed to (these higher level transformations themselves may have their own evolutions, in the case of Sophix and Lovix for Believix).
Works Only On Earth?
It has widely been rumored that Believix is a transformation which works only on Earth. However this seems unlikely, as such a thing was never mentioned anywhere in the series, and in the first episode of Season 4, Miss Faragonda had already mentioned this transformation to the Winx even before they first met the Wizards of the Black Circle and hence decided to go to Earth. This suggests that Believix is not specific to Earth, but instead can be more easily gained on Earth since people no longer believed in magic there, and that it could also be earned anywhere where people do not believe in magic and that once earned it can be used anywhere in the Universe as its powers do not limit themselves only to make people believe in magic, but also to open the hearts of people to good feelings.