Although not used in everyday discussions as it was in the past, this idiom is still used in the legal system. In this reduplicative phrase, common since the 14th century, the nouns ‘part’ and ‘parcel’ are synonyms. It comes from the ancient legal practice of including words of closely similar meaning to make sure that the sense covers all eventualities. The expression part and parcel was originally used in a sense that was frequently preceded by every, to mean all parts of something, even the smallest.
A parcel is part of a larger whole, such as parcel of land, parcel of weather, parcel of equipment, etc. Part is a division or portion of something and has the same meaning.
Recently it has come to imply the sense of something being a necessary part of some larger containing thing and the implication that this particular part may not be desirable, but cannot be avoided if you want the thing it is part of. For instance, we understand that some inconveniences are still part and parcel of modern travel. Other similar words include: nooks and crannies, aid and abet, etc.
Incidentally, the Southern US variation, passel comes from the old pronunciation of parcel and is often preceded by whole, suggesting a large group of people or things, such as a passel of problems, or passel of experts.