Today's word is primus - and note that the i is long: prīmus, prīma, prīmum.
This is an incredibly productive word root in Latin, and is also involved in innumerable English words borrowed from Latin. There is also a Latin phrase that we still use in English: prima facie.
The word in Latin is actually a sneaky kind of superlative: the "mus" ending that you see there is actually the same as the "mus" ending that you find in superlative adjectives: fortissimus, optimus, primus. The English word "first" is also a superlative, with the same "st" that you see in other English superlatives like "fastest," "best," etc. That's why you cannot be "firstest" in English, ha ha.
So, with the Latin primus, what we are probably dealing with here is an archaic preposition that has fallen out of use - pri - but which we can still see in these derivative forms that relate to being first in line, ahead of other things, such as prior and priscus. The preposition pri has not survived, but instead we have similar prepositions such as pro and prae.
So, something that is primus is the most "pri" of all, the thing that is absolutely first.
This might be something first in a sequence, like the way A and B are the first letters of the alphabet, primae litterae.
You can also have things first in time: primo tempore, meaning "at the first opportunity" or a primo, "from the first, from the beginning." Something primitivius in Latin is the thing first-born in time, such as the flores primitivi, the flowers that bloom first, ahead of the others.
Things can also be first (or forward) in space: primus digitus is the tip of your finger.
There is also a value judgment implied here: things that are first are also best. This is where we get the word princeps, for example, the "first" guy, the "number one" guy - which is where we get "prince" in English.
There are quite a few adverbial expressions created from this word, including primum and primo, and also (more rarely) prime and primiter.
Here are some examples of today's word in Latin sayings and proverbs; for more information, see the page at the Scala Sapientiae, which contains notes on some of the proverbs cited below, as well as additional proverbs:
Primus sum egomet mihi.
Non possunt primi esse omnes omni in tempore.
Erunt novissimi primi, et primi novissimi.
Primo quoque die nemo magister erit.
Nemo primo quoque die fit doctus.
Primus amor potior.
Nemo potest scire, quis primus debet abire.
Primus inter pares.
In bello nec primus nec ultimus esto.
Primus beatus qui per se sapiat, secundus qui sapientem audiat.
Primum: non nocere.
Prima virtus est vitio carere.
Vis loqui? Disce tacere primo.
Offeras primum pacem.
Morbum suum nosse est pars prima salutis.
Alium silere quod voles, primus sile.
Primum est suo esse contentum.
Primum hominis officium est suo esse contentum.
Prima virum primum mulier deiecit ad imum.