Today's word is DIES, which is a fifth-declension noun, genitive diei. You can see the noun declined at the Wiktionary. Unlike other fifth-declension nouns, dies is found both as a masculine noun and as a feminine noun.
Latin meaning and usage: The basic meaning is the 24-hour period day, but it can also mean the day as opposed to the night.
Latin word formation: The word dies appears in various compounds: hodie, pridie, cottidie, postridie, nudius (nunc dies), and meridies. The adverb diu and adjective diurnus are also derived from this word.
English cognates and derivatives: One of my favorite Latin derivatives is English "dismal" which comes from Latin dies mali. We have the adjectives "diurnal" and "circadian" (circa diem), and the noun "diary" from Latin diarius. Likewise, we have the word "dial" from Latin dialis. The word "Noel" is from natalis dies. Our word "meridian" is from meridianus, the adjectival form of meridies.
Here are some examples of today's word in Latin sayings and proverbs; for more examples, see the page at the Scala Sapientiae, which also contains notes on some of the proverbs cited below:
Nullus agenti dies longus est.
Vive in diem.
Noctem dies sequitur.
Dies diem docet.
Stat sua cuique dies.
Nox tibi longa venit nec reditura dies.
Lumen Dei, lex diei.
Nemo nisi suo die moritur.
Primo quoque die nemo magister erit.
Nemo primo quoque die fit doctus.
Diem nox premit, dies noctem.
Roma non fuit una die condita.
Roma non uno condebatur die.
Tenere non potes, potes non perdere diem.
Breves dies et horae omnia sunt.
Singulos dies singulas vitas puta.
Omnes dies pauperis mali.
Nil agenti dies longus est.
Summum nec metuas diem, nec optes.