Immaculate Conception and Assumption

One 'problem' that some non-Catholics have with our faith is our devotion to the Virgin Mary. The two most important Marian doctrines that they seem to object to is the Immaculate Conception and Assumption.

(from Catholic Answers):
Immaculate Conception: It’s important to understand what the doctrine of the Immaculate Conception is and what it is not. Some people think the term refers to Christ’s conception in Mary’s womb without the intervention of a human father; but that is the Virgin Birth. Others think the Immaculate Conception means Mary was conceived "by the power of the Holy Spirit," in the way Jesus was, but that, too, is incorrect. The Immaculate Conception means that Mary, whose conception was brought about the normal way, was conceived without original sin or its stain—that’s what "immaculate" means: without stain. The essence of original sin consists in the deprivation of sanctifying grace, and its stain is a corrupt nature. Mary was preserved from these defects by God’s grace; from the first instant of her existence she was in the state of sanctifying grace and was free from the corrupt nature original sin brings.

Assumption: The doctrine of the Assumption says that at the end of her life on earth Mary was assumed, body and soul, into heaven, just as Enoch, Elijah, and perhaps others had been before her. It’s also necessary to keep in mind what the Assumption is not. Some people think Catholics believe Mary "ascended" into heaven. That’s not correct. Christ, by his own power, ascended into heaven. Mary was assumed or taken up into heaven by God. She didn’t do it under her own power.

The whole tract on this topic is on Karl Keating's (Catholic apologist) Catholic Answers website. You can read it here.