The third day of the week, as it was named by the Shire-hobbits at the end of the Third Age. The similarity to our own modern 'Monday' is not coincidental: both are days originally dedicated to the Moon. The form used in the Shire dated back to an original Common Speech form Monendei. That old form was itself a translation of the original Elvish day-name, which was Isilya in Quenya, or Orithil in Sindarin.
Notes
1
Despite its spelling, most English-speakers pronounce the word 'Monday' as 'mu'nday' rather than 'mo'nday' (that is, with an 'u' sound rather than an 'o'). Since the Hobbits' version of the name had different etymological roots, it is hard to say whether the same convention would apply. Given that Tolkien designed the Hobbit day-names to mirror our own, on balance it seems most likely that the typical English 'mu'nday' is intended. (Barliman Butterbur uses the phrase 'a month of Mondays' in The Return of the King VI 7, Homeward Bound, which - given that the modern equivalent is a 'month of Sundays' - does seem to imply that 'Monday' should rhyme with 'Sunday'.)