"In my childhood I met a wizard."
When he was 9 years old, he got critically injured in an "accident". Then he "miraculously" recovered. During this, he got a strange ability. It is called (laterally) "Magical eyes of the direct death" (or such, beyond my English). He see the lines where objects break easily. If he cut the line with knife, object "dies". At cost of his health (or maybe sanity), he can kill anything...
After he recovered from injury, he adopted to Arima family, one
of a branch family of Tohno, because his bad health wasn't deserve as the head
of Tohno family.
Eight years after, when his father Makihisa died, he was called back to Tohno
family by Akiha who is now the head of family (actually, only Akiha and Shiki
are alive as pure Tohno's).
The story of Tsukihime starts when he was called back to Tohno's mansion.
Shiki isn't real child of Tohno family (and he isn't Akiha's blood brother). He was born as a child of Nanaya family.
Nanaya family is "demon hunter" lineage, though now
Shiki is only one survivor. Shiki was trained as fighter or assassin in his
childhood (though this memory was erased when he adopted to Thono family). Nanaya
family has some special ability, in this case called "psionics", by
which they can see something normally invisible.
And they have "murder impulse" to monsters, like vampires or demons.
He was adopted to Tohno family because Makihisa thought "it's interesting, this boy has a same name of my son.". Yes, there are another Shiki in Tsukihime story, and this is very important part of story.