Achika Masaki was Tenchi's mother and Yousho's daughter. The reason she was Tenchi's mother, rather than is, is that sadly she passed away when Tenchi was still young. As a result, Tenchi was raised mostly by his father Nobuyuki and his grandfather Yousho through much of his life.
What is known about Tenchi's mother is what is gleaned through flashbacks that Tenchi has of his mother Achika. Tenchi remembers his mother as someone who was gentle, and there is no doubt that there was a lot of love between Achika and her son Tenchi. Achika's death really hit Tenchi very hard, as was seen in Ryouko's flashback of Tenchi's childhood where Tenchi was seen crying upon the entrance of the cave after his mother's death. Tenchi still keeps several of his mother's belongings, such as the kimono her mother wore. He treasures each of his mother's things, and when Ryouko accidently ruined his mother's kimono, Tenchi yelled that he hated Ryouko, something he would never do under any other circumstance.
Being Yousho's daughter, Achika was also part Juraian, and thus should have inherited the throne and the power Tenchi presently acquired. However, she had wanted to live a normal life and wanted no part in the Juraian court. After marrying Nobuyuki, her birthright was then passed on to Tenchi. Several sources, such as Tenchi 101, state that Achika tried to go through the same test Tenchi did to acquire the Juraian heritage, but since she had wanted to live a normal life, she was unsuccessful in the test. Her early death is presumed to have been a side effect of failing the test.
Most people, however, are more familiar with the Achika presented in the movie Tenchi Muyo in Love, so the following section will go on to describe the Achika presented in the movie. In the movie, Achika was still the daughter of Yousho, and thus she had the power of Jurai within her, though it had not been awakened. She fell in love with Nobuyuki, who in his youth was a very shy young man who aspired to be an architect. However, an entity known as KANE planned to kill Achika since her ancestor, the emperor of Jurai, had assisted the Galaxy Police in capturing KANE, though he lost his life in the process. Tenchi and his friends go back in time to stop KANE, and the final battle occurs in subspace. Nobuyuki had been seriously injured, and seeing Nobuyuki in his injured state, the power within Achika was awakened, and donning a traditional Juraian kimono, she defeats KANE using Tenchi's sword Tenchiken. However, as a result of using the power of Jurai, Achika's life was shortened, and she passed away when Tenchi was about six years old.
No matter which version of Achika's history appeals most to you, there is little doubt that she was a very kind, gentle, and caring individual. The fact that Tenchi still treasures the memories he has of her, even though she passed away when he was still young, is testament to the tremendous love displayed between mother and son.