in the Bible, is usually,

An offering made to God by killing and burning some perfectly unblemished animal on an altar, as an acknowledgment of God's power, to make up for sins, or to gain favor, etc.  These types of sacrifices were once necessary for the Jews,
before Christ came.  They are now no longer necessary for Christians, as Jesus came
and sacrificed Himself  as the
perfect sinless Lamb,
once for all.
I beseech you therefore, brethren,
by the mercies of God,
that you present your bodies a living sacrifice,
holy, acceptable unto God,
which is your reasonable service. 
And be not conformed to this world:
but be ye transformed by the renewing of your
mind, that ye may prove what is that
good, and acceptable, and
perfect, will of God.

Another type of

is, to give up something for another,
such as giving up sin to please God,
or, giving up pleasure time to help someone in need, or, suffering
some other loss for the
sake of another.