Sunday: Old English Sunnandæg, meaning "Sun's Day". This is a translation of the Latin phrase diēs Sōlis. English, like most of the Germanic languages, preserves the day's association with the sun. Many other European languages, including all of the Romance languages, have changed its name to the equivalent of "the Lord's Day" (based on Ecclesiastical Latin dies Dominica). In both West Germanic and North Germanic mythology, the Sun is personified as Sunna/Sól.
Monday: Old English Mōnandæg, meaning "Moon's Day". This is equivalent to the Latin name diēs Lūnae. In North Germanic mythology, the Moon is personified as Máni.
Tuesday: Old English Tīwesdæg, meaning "Tiw's Day". Tiw (Norse Týr) was a one-handed god associated with single combat and pledges in Norse mythology and also attested prominently in wider Germanic paganism. The name of the day is also related to the Latin name diēs Mārtis, "Day of Mars" (the Roman god of war).
Wednesday: Old English Wōdnesdæg, meaning the Day of the Germanic god Woden, and a prominent god of the Anglo-Saxons in England until about the seventh century. This corresponds to the Latin counterpart diēs Mercuriī, "Day of Mercury", as both are deities of magic and knowledge. The German Mittwoch, the Low German Middeweek, the miðviku- in Icelandic miðvikudagur and the Finnish keskiviikko all mean "mid-week".
Thursday: Old English Þūnresdæg, meaning 'Þunor's day'. Þunor means thunder or its personification, the Norse god known in Modern English as Thor. Similarly Dutch donderdag, German Donnerstag ('thunder's day'), Finnish torstai, and Scandinavian torsdag ('Thor's Day'). "Thor's day" corresponds to Latin diēs Iovis, "Day of Jupiter" (the Roman god of thunder).
Friday: Old English Frīgedæg, meaning the Day of the Anglo-Saxon Goddess Fríge. The Norse name for the planet Venus was Friggjarstjarna, 'Frigg's star'. It is based on the Latin diēs Veneris, "Day of Venus".
Saturday: named after the Roman god Saturn associated with the Titan Cronus, father of Zeus and many Olympians. Its original Anglo-Saxon rendering was Sæturnesdæg. In Latin, it was diēs Sāturnī, "Day of Saturn". The Nordic laugardagur, leygardagur, laurdag, etc. deviate significantly as they have no reference to either the Norse or the Roman pantheon; they derive from Old Nordic laugardagr, literally "washing-day". The German Sonnabend (mainly used in northern and eastern Germany) and the Low German Sünnavend mean "Sunday Eve"; the German word Samstag derives from the name for Shabbat.
January and March honor the Roman gods Janus and Mars.
February may derive from the Roman Februa festival (for purification).
April may relate to the Etruscan goddess Apru or the verb aperire ("to open").
May and June may honor Maia and Juno or derive from archaic terms for "senior" and "junior".
July and August honor Julius Caesar and his successor, the emperor Augustus.
September, October, November, and December are formed from the numbers from 7 to 10, their position in the calendar when it began around the spring equinox in March.