Dragon Ball Z Kai is an edited version of the popular anime Dragon Ball Z. Kai removes the filler(episodes which do not advance the plot) from Z, making it closer to the manga's story.
As for how safe this show is for children, it really depends on which version of Dragon Ball Z Kai you are watching. Certain versions, such as the nick toons edit, remove blood, profanity, and suggestive language to a certain degree. This review, however, concerns the uncut, original version of the show.
Dragon Ball Z Kai is an action show which focuses on martial arts. Naturally, violence is nearly always present in the show as the characters are constantly fighting enemies. Some mild profanity occasionally occurs. One side character, Master Roshi, is a pervert and makes many suggestive comments and acts perverted towards other female characters. Please note that Roshi rarely shows up in the entirety of the show and he is not present for almost entire seasons of the show. Some characters are shown drinking but, as far as I recall, the show never explicitly calls the beverage alcoholic. Multiple characters are also either heavily or injured or killed. Those who are killed are shown passing into the "next world", which is Kai's portrayal of the afterlife. There is virtually no consumerism in this show, as it takes place in an "alternate Earth". Practically all products are made by the fictional company "Capsule Corporation" which is run by the recurring character Dr. Brief, father of side character Bulma.
The show's conflicts mainly stem from the theme of "Good Vs. Evil". Goku, the show's main character, is constantly training to become the greatest martial artist and never stops believing in himself. Though he is usually outclassed by the current villain, his tenacity allows him to overcome any obstacle, including the villain.