The last day but one of the ancient Shire-names for the days of the week, which by the end of the Third Age had evolved into 'Mersday'. It was a day dedicated to the Sea (though the Shire lay far inland, and in fact it was exceedingly rare for a Shire-hobbit to see the ocean even once in their lives). It was derived from the Elvish day-names Eärenya or Oraearon, introduced into the calendar originally by the mariners of Númenor, and handed down through tradition even after the Downfall of their land.
Notes
1
According to Appendix D to The Lord of the Rings, day-names like Meresdei were in use at least some nine centuries before the end of the Third Age. Across the period that followed, the names of the days evolved into simpler forms, so Meresdei would become Mersday by the Age's end.
2
Our only specific record of this usage is from the history of the Shire. Its use in Buckland or the Bree-land seems likely, but is not directly attested. For further discussion on this point, see footnote 2 to the entry for Sterrendei.
3
All the vowel sounds in this name should be pronounced independently, so in full the name would be pronounced as 'me-res-die', not 'meers-die'. As shown here and above, the final syllable is pronounced like the English word 'die'.