An altar is a table or place which serves as a center of worship or ritual — often used with the to refer to the act of getting married. Here's the altar at my little church at Christmas:
Sometimes people will talk about it a bit more figuratively:
A raised structure (such as a block, pile of blocks, pillar, or stand) on which sacrifices are offered or incense burned (as in the worship of a deity or of the spirit of a deceased ancestor) — often used figuratively to describe a thing given great or undue precedence or value especially at the cost of something else <He sacrificed his family life on the altar of career advancement.>
But when you use alter, you are performing an action - to cause to become different in some particular characteristic (as measure, dimension, course, arrangement, or inclination) without changing into something else OR to become different in some respect : undergo change usually without resulting difference in essential nature.
So if you want to see what happens when you alter an altar, here you go: