Short answers, pulled from the story.
Huginn and Muninn translate roughly as "mind and will" in Old Norse. Huginn derives from hugr, covering meanings such as thought, perception, mood, and desire. Muninn derives from munr, covering affection, intent, memory, curiosity, and prediction. The two words overlapped considerably and were likely close to synonyms.
Huginn and Muninn fly across the entire world (Midgard) every day and return by dinner-time to report everything they have seen and heard to Odin. This daily intelligence-gathering is why Odin earned the byname Hrafnaguð, meaning raven-god. According to Heimskringla, Odin also gave the ravens the gift of speech.
Huginn and Muninn appear in the Poetic Edda (compiled in the 13th century from earlier sources), the Prose Edda, the Heimskringla, and the Third Grammatical Treatise compiled by Óláfr Þórðarson. They also appear in the poetry of skalds, including excerpts from a work by Einarr Skúlason preserved in the Prose Edda.
Possible depictions appear on Migration Period gold bracteates from the 5th and 6th centuries found across Denmark, Sweden, Norway, and England; Vendel era helmet plates from the 6th or 7th century found in Sweden; Iron Age bird-shaped brooches from Bejsebakke in northern Denmark; fragments of the Oseberg tapestry from Norway; and a niello-inlaid silver figurine dubbed "Odin from Lejre" announced by the Roskilde Museum in November 2009.
Thorwald's Cross is a partly surviving runestone erected at Kirk Andreas on the Isle of Man. It depicts a bearded figure holding a spear at a wolf, with a large bird on his shoulder. Andy Orchard suggests the bird may be either Huginn or Muninn. The Scandinavian Runic-text Database dates the cross to 940, while another scholar dates it to the 11th century.
John Lindow connects the ravens to shamanic trance-state journeys. Anthony Winterbourne links them to the Norse fylgja (a guardian spirit with shape-shifting abilities) and the hamingja (a ghostly animal double). Rudolf Simek instead ties them to broader Germanic raven symbolism, including the raven banner. Biologist Bernd Heinrich proposes they reflect an ancient hunting symbiosis among ravens, wolves, and humans.