A fixed point in time is an event that's so crucial to the integrity of the universe's timeline that it must happen & cannot be prevented without disastrous consequences. The consequences of attempting to prevent such an event were shown in "The Wedding of River Song". Different eras became jumbled up together, the entire timeline became unstable & was collapsing.
Although a fixed point must happen, some of its details can be changed. This was shown in "The Fires of Pompeii" & "The Waters of Mars". (The difficulty is in knowing which details can be changed & which cannot.)
A fixed point can be created from a "still point" in time, but what exactly a still point in time is is unknown. The fixed point River tried to prevent in "The Wedding..." had been deliberately created in this way. The same story also showed that the event concerned may not be what it appears to be or what it was intended to be. (Instead of the Doctor being shot to death, the event was actually the Teselecta, wearing the form of the Doctor, being shot.)
As the Doctor explained to Jack Harkness in "Utopia", a person can also be turned into a fixed point -- but should not be. When Rose (as the Bad Wolf) used the power of the vortex to bring Jack back to life in "The Parting of the Ways", she overdid it & brought him back forever. As a result: "You're a fixed point in time and space. You're a fact. That's never meant to happen."