B.C. means "Before Christ" in the sense that the year Jesus of Nazareth was at one time thought to have been born corresponds with what would be the year zero (if there were one), so the period before that year was before Christ. B.C. is roughly the same as B.C.E. (Before the Common Era).
When writing it out, "B.C." follows the date. "It is tradition that Rome was founded in 753 B.C."
If the terms A.D. and B.C. confuse you, think of a number line
- _______0_______ +
with A.D. on the plus (+) side and B.C. on minus (-) side. Unlike the number line, there is no year zero.
-4 -3 -2 -1 0 +1 +2 +3 +4
3BC 2BC 1BC AD1 AD2 AD3