Copii= children (plural form ending in -i)
Copiii= the children (the articol in Romanian is usually at the end of the work and not before it therefore another -i is put there to represent that). You also need to pronounce two -i when speaking.
Bert, in Romanian, when a noun stands for a subject, it is always used with a definite article, unlike in English, when the use of the article is conditioned by the meaning of the sentence. I hope this was helpful.
As far as I can tell, definite form is used for expressing general concepts, and in this sentence, children are referred to as such, i.e. it's not any specific children we refer to, but children in general.