Most of what we know of Norse mythology comes from two sources: the Prose Edda and the Poetic Edda.
What is the difference between the two?
Wikipedia answers this sufficiently:
The Poetic Edda is the modern attribution for an unnamed collection of Old Norse poems. Several versions exist, all consisting primarily of text from the Icelandic mediaeval manuscript known as the Codex Regius.
The Prose Edda, also known as the Younger Edda, Snorri's Edda or simply Edda, is an Old Norse work of literature written in Iceland in the early 13th century. Together with the Poetic Edda, it comprises the major store of Scandinavian mythology. The work is often assumed to have been written, or at least compiled, by the Icelandic scholar and historian Snorri Sturluson around the year 1220.
The Prose Edda is related to the Poetic Edda in that the Prose Edda cites various poems collected in the Poetic Edda as sources.
If you are interested in a closer look, you may find English translations of both on sacred-texts.com:
The "Poetic Edda" is used to refer to a group of poems dealing with the Norse Gods and heroes. There doesn't seem to be a single version, but all versions draw from the Codex Regius. Although the Codex was written in the 13th century, the material it is comprised of may be older, as Old Norse poetry dates as far back as the 8th century. The poems constitute what may be termed "Eddaic poetry" as opposed to the more complex "skaldic poetry". The poems themselves are unattributed and the author Codex is unknown.
The Prose Edda, by contrast, is attributed to Snorri Sturluson, although he may have simply compiled it, as opposed to having been the author. The stories contained in the Prose Edda are more detailed and reflect the more sophisticated narrative techniques of later generations. (The Icelandic Sagas, in particular, can be viewed as a precursor to the modern novel.) Although the Prose Edda certainly draws from the poems of the Poetic Edda, it also includes many embellishments.
From a personal standpoint, I feel that the Poetic Edda is similar to Classical work such as the Homeric Hymns which are more formal and have a religious context. The Prose Edda, by comparison, provides more detailed and engaging narrative similar to, say, the Odyssey, although it is a collection of stories as opposed to a single epic, with the entertainment of the reader/listener as the primary intent.
For the Norse Mythology experts, please feel free to make corrections if the are any inaccuracies in this answer! My intent is to provide helpful context beyond the bare facts.