"De" in this sentence points out that it is some particular cups.
Examples: "De vakre kvinnene bruker kjoler" - "The beautiful women wear dresses" If you drop "De", it would be "Vakre kvinner bruker kjoler" - "Beautiful women wears dresses" And suddenly - it is not definite anymore. Unfortunately, I can't tell you the rules here :(
'tomme' is plural of 'tom': Adjectives change depending on the gender and number of the noun.
En tom koppen = an empty cup (masculine)
Tomme kopper = empty cups (plural)
Et tomt hus = an empty house (neuter)
Ei tom flaske = an empty bottle (feminine)
(feminine and masculine are often, maybe always, written the same)
There is a weird rule in Norwegian that a word should never end with two 'm's, so when the base word ending in '-m' gets an extra vowel letter (in this case -e), you must also add a second m, so you get 'tomme' instead of 'tome'. This is a special case which only happens with the letter 'm'.
So many up-votes make me think I've missed something here, but your "weird rule" does not make sense. You say a word should never end with two 'm's. If you add an 'e' to 'tom', you would have 'tome', which ends in 'me', not two 'm's. So where is the problem? Or... how does your rule about two 'm's apply here? Sorry for not getting it...
In writing, you'll have to rely on context. If there is none, one would default to "the" as the most likely option.
In speech, "de" will be stressed when meaning those, and the speaker may even point at the X in question to clarify that they mean those in particular.
Note that while the above holds true for a "de + [adjective] + [noun]" construct like the above, "de koppene" without the adjective will always mean "those cups", as "the cups" is just "koppene".