The invocation serves a couple of purposes in Paradise Lost. Because Milton sets out to write Lost as an epic poem, he follows the traditions of epic poetry. One major element is a call upon the muses to help the poet tell his story. In this case, Milton invokes the Muse's help since he was not present when the infamous battle occurred between God and Satan or the creation of the earth. Thus, Milton's main purpose for including an invocation is a stylistic one--he simply follows the format of all great epic poems (The Odyssey, Beowulf, etc.).
Secondly, in Book One, Milton enunciates his goal in writing the poem and presents a disclaimer of sorts. He wants readers to know the complexity and difficulty of his attempt to write not only an epic poem but also to write on the subject of man's fall.
The purpose of Book 1 was to outline the chain of events that led not only to the fall of man but also that of Satan. Satan’s pride made the angel to lead a rebellion against God. Satan was jealous of the Son and God’s favor upon him. Satan marshaled other rebellious angels and waged war in Heaven. The conflict forced God to involve the Son in order to end it. The Son goes to battle and defeats Satan and his followers and casts them into the deep fiery pits of Hell.
Satan and his followers feeling dejected, plot to rise against God’s throne. Satan remembers prophesy about the new existence of God’s creation known as man. He informs the other cast out angels of his plan to find man so he can turn the race from God as an affront to the Most High. Satan employs mischief against Uriel to find out where man lives and pursues them in the Garden of Eden. God on the other hand employs Raphael to warn Adam of the impeding danger due to the fall of Satan. Book 1 provides the basis and motivations of Satan’s conflict with God and the continuation of this conflict through man and the opportunity for man’s redemption