"Tuesday is a day of the week."
Translation:Marți este o zi a săptămânii.
Ok, so there's a lot to unpack here.
"De" doesn't count here because "de" is usually used as "consists (entirely) of": un pahar de lapte (a glass of milk).
What we actually want to say is "day of the week" in terms of "day belonging to the week". To do this, we us a posessive pronoun: "a" (fem. sing. posessive article followed by the noun owning that item.
In our case, that would be "a săptămâna"
But it's made a bit more complicated... The noun appears in its dative form, i.e. it's not the object of the sentence: "Tuesday" is. So we use the definite genitive form of "week": săptămânii
At least this is how I understand it. Noun cases are quite confusing even at the best of times, and are covered in future lessons.
I'll try and explain "din săptămână" in a separate comment.
This form (zi de...) is used when you have to accurately indicate a certain time interval (a season, or a month), such as "Era o frumoasă zi de iarnă" or "Ne-am văzut într-o zi de aprilie". You will never hear "Marți e o zi de săptămână (de lună, de an)" because this sentence says nothing.
It changed to săptămânii due to the noun being used in a possessive sense. So, the possessive situation puts us in the genitive case. Therefore, the genitive form of the noun is required. Here, we are saying the "day of the week" or the "week's day." The week sort of possesses or "owns" the day. "Din" would be used if the day were coming out of a container or something like that (ok, obviously an oversimplification). We are not saying the "day FROM the week" but rather "the day OF the week."