The following information is mostly ganked from the entry over at Wikipedia. Feel free to shoot over there for further details about this and other sentai series.
A war between Infershia and Magitopia had occurred unbeknownst to humans. The Infershia have returned to get revenge from their imprisonment. When the Infershia attack, five siblings witness their mother change in front of them and she hands them MagiPhones to transform into a magic team. Now endowed with magic powers, these five vow to live up to their family's legacy.
These five children (three brothers and two sisters) lived peacefully with their mother, on the notion that their father died in an expedition in Antarctica. But upon learning the truth, their mother revealed to them their family legacy: they were the descendants of a long line of magicians.
Kai Ozu/MagiRed: The youngest, Kai is a Red Mage, a wizard who has power over fire. He's a sophomore student who's into soccer and fights a lot with Tsubasa. He's straightforward and is impulsive, which often leads to him making mistakes, but he is also kind-hearted and very brave for his age. He hates to be babied and wants to be treated like an adult. He was most upset about his mother's death by Wolzard, and swore vengeance for it, until he learned that Wolzard was his father. He has a special talent for Alchemy. His primary attack is "Red Fire," where his body is engulfed in flame creating a phoenix which flies through and burns any adversary.
Tsubasa Ozu/MagiYellow: The 4th born, Tsubasa is a Yellow Mage, a wizard who wields the power of thunder and lightning. He's intuitive, a realist and usually rational. He looks at life crossways, is a bit closed in himself, cynical and sarcastic. His special talent is potion work. His primary attack is "Yellow Thunder," where he shoots a barrage of lightning arrows from his Magistick Bowgun.
Urara Ozu/MagiBlue: The 3rd born, Urara is a Blue Mage, a sorceress with power over the water. She has a gentle heart, acting like mother sometimes. She's a passive sort, listening to the others and holding her tongue, hiding her own feelings of hurt and distress until they boil over and she explodes. Her special ability is fortune telling and prophecy. Her primary attack is "Blue Splash," which acts two ways, either a high powered stream of water or a barrage of exploding geysers.
Houka Ozu/MagiPink: The 2nd born, Houka's a Pink Mage, a sorceress with power over the wind. She is cheerful and flighty, stringing along several boyfriends. She has a narrow focus, though, and can be a troublemaker. She works as a fashion model when she feels like it. She also has a talent for transformation magic, turning herself into any form she can imagine. Her primary attack is "Pink Storm" where she transforms into an electric fan and blows way the bad guys.
Makito Ozu/MagiGreen: The 1st born, Makito's a Green Mage, a wizard who wields the power over the earth. He spent his life growing vegetables on his property, Aniki Farm, and cooking delicious meals with his own hands. He's usually a cheerful fellow, but moves along at a rather slow pace, taking it easy through life. However, he does have a nasty temper and can get on people's nerves. He tends to be like a father to his siblings. Initially, he as a strong dislike for Hikaru, feeling taken over as head of the household, and in the heart of his girlfriend Erika. His special talent involves Herbology. His primary attack is "Green Gound" where he creates an ground shockwave by slamming his Magistick Axe against the ground.
Miyuki Ozu/MagiMother: A strong, gentle, ideal mother, she raised her five children alone after Isamu disappeared. She kept many secrets from them, not the least of which was the truth about herself. She was a White Mage, a sorceress wielding the power of ice magic from a long line of magicians who protect the world from the Infershia. She wore white armor with a snowflake emblem on her helmet and wand. She was seemingly killed by Wolzard, but in reality, her death was faked with her MagiStick remaining to have the siblings believe their mother was killed.
Isamu Ozu/Magical Knight Wolzard: A mysterious figure who first appeared to work for the Infreshia as their most important member. Wolzard was a black mage, a wizard who weilds power over darkness. At first, he usually fought MagiRed, as he wanted to avenge his mother's death and defeated Wolzard 1-on-1. He mysteriously disappeared after Branken's defeat until he reappeared a little after Memmi took over. He can enlarge himself and combine with Valkirion to become either WolKentaurus or WolKaiser. Over time, Wolzard's identity was finally revealed as the MagiRangers' father. His real name is Bragel, the Sky Saint who sacrificed himself to have the Inferno Gate sealed to keep N-Ma from entering the human world. But within the gate, Bragel was finally defeated by the Four Beastman Kings and was transformed into Wolzard by N-Ma. Kai managed to free his father from the Mado spell over him. He was thought to had apparently died in battle, but he returned to help his children fight the Pantheon in a new Red form, Wolzard Fire.
Hikaru/MagiShine: His real name is Sungel, a Sky Saint who wields the power of light. He was transformed into a frog by Raigel 15 years ago, only to be restored by MagiBlue, as only a Blue Mage's kiss can break the spell. He currently lives with the Ozu siblings as their mentor in the ways of magic and comes to their aid when he's needed. Though not related to the Ozu family, he considers his mentor Brajiel as a father-like figure.
Mandora Boy: A young Mandrake the MagiRanger met when they found their secret headquarters. Despite being in a pot, he can hop around as well as fly.
Smoky the Magical Cat: Hikaru's mischievous feline genie who resides in the MagiLamp, which was found in the cave that was Raigel's tomb. He came into being from a volcano in Magitopia. He gathered piles of treasures until one day he opened a pandora's box and doomed himself to a slow death. To save him, Sungel sucked him into the MagiLamp. Smoky was spared, but he can't last out of the lamp for more than three hours. However, Smoky can be released from the curse if he grants the wishes of others, but Smoky prefers to grant only one wish to whoever awakens him from his slumber, and only if he is compensated for his services. The Ozu gang wish for the Infershia to be gone, and he denies their request, stating that the power the Infershia wield is greater than his own. Despite being a goof-off, he is a capable fighter and once piloted Travelion. He sees Urara as a mother figure and bickers with Mandora Boy now and then.