Between the 1st and 3rd centuries, the Roman Empire gradually replaced their previous system with a 7-day week with each day named after the planets of Hellenistic Astrology: The Sun, The Moon, Mercury, Venus, Mars, Jupiter and Saturn.
When the Germanic culture came in contact with the Romans, there was a practice where Germanic deities were identified with Roman equivalents. This process was known as Interpretatio germanica.
The Germanic peoples adapted the 7-day week system from the Romans and substituted the Roman gods with Germanic equivalents, except for Saturday, which retained the Roman god's name. This process happened after 200 AD but before the introduction of Christianity to Germanic peoples during the 6th to 7th century.
If the Latin influence was strong enough to supply the original meaning for the word, then why didn't they simply borrow the actual Latin word and instead ended up translating it into the Germanic equivalent?
The answer is likely cultural pride. It's likely the Roman system was adapted for reasons of trade, convenience or war — but would you want to retain the names of the gods of your neighbours/enemies in the days of the week?
In other [words], why didn't we end up with something like "lunday"?
Mēnô was the Germanic moon deity (alternate spellings include Máni, Mōna, Māno,) so that's why dies Lūnae became Mōnandæg in Anglo-Saxon.
Why was Sæturnesdæg the only day that retained the Latin god's name? Probably because there was no Germanic god associated with Saturn.