Learn Hardcore Romanian: Bagajul este greu.

It’s the definite article for masculine singular nouns. Romanian attaches -ul to a noun to make it “the” noun. So bagaj = “a bag/luggage,” and bagajul = “the bag/luggage.”

Why is este used instead of e?

Both are forms of the verb a fi (“to be”). Este is the full form you’ll see in writing and in formal speech. E is the contracted, colloquial form used in everyday conversation:
Bagajul e greu.

What part of speech is greu, and how does it agree with bagajul?

Greu is an adjective describing weight. In Romanian adjectives agree in gender and number with the noun:

Masculine singular: greu (bagajul este greu)
Feminine singular: grea (valiza este grea)
Masculine plural: grei
Feminine plural: grele
Since bagaj is a neuter noun (behaves like masculine in singular, feminine in plural), you use greu for singular and grele if you turn it into a plural noun.

Why is the adjective greu placed after the noun?

The default word order in Romanian is Noun + Adjective. Adjectives normally follow the noun they modify, though you can move them before for emphasis or stylistic effect.

How would you form the sentence “The bags are heavy” in Romanian?

Plural of bagaj is bagaje, and the definite article becomes -le, giving bagajele. The verb switches to sunt (they are), and the adjective to grele (feminine plural agreement for neuter plural nouns):
Bagajele sunt grele.

How can you say “It’s heavy” without explicitly mentioning bagajul?

You simply drop the subject and say E greu (colloquial) or Este greu (formal). The context tells your listener what “it” refers to.

How do you say “A bag is heavy” or “Some bags are heavy” with an indefinite article?

“A bag is heavy” = Un bagaj este greu.
“Some bags are heavy” = Niște bagaje sunt grele.
Romanian uses un for “a/an” (singular) and niște for “some” (plural).

What is the difference between bagaj and valiză?

Bagaj (neuter) means “luggage” or “a (piece of) baggage” in general.
Valiză (feminine) specifically means “suitcase.”

How would you say “This luggage is too heavy” in Romanian?

Use the demonstrative acest for masculine/neuter nouns and prea for “too”:
Acest bagaj este prea greu.

What is the opposite of greu, and how would you say “The bag is light”?

The opposite adjective is ușor (“light” in weight). You’d say:
Bagajul este ușor.