Learn Romanian: E important să termini completarea acestui formular. - It is important to finish the completion of this form.

This is a "long infinitive" noun, which turns an action into a concept. You take the infinitive verb a completa (to complete) and add the -re suffix to make the noun completare (completion). Because we need to say "the completion" in this sentence, we add the feminine definite article -a to the end, giving us completarea.

Why does the sentence use acestui formular instead of just acest formular?

It is in the Genitive case, which indicates a relationship like "of" in English. Because you are talking about the completion of this form, the noun completarea forces the following phrase into the Genitive case. For a neuter noun like formular, the demonstrative adjective acest (this) changes to its Genitive form, acestui.

English says "to finish", so why does Romanian use the subjunctive să termini instead of an infinitive?

In Romanian, impersonal expressions like e important (it is important), e bine (it is good), or e necesar (it is necessary) are almost always followed by the subjunctive (să + verb). So while English says "It is important to finish", Romanian phrasing translates more like "It is important that you finish".

Could I just say să completezi acest formular instead of using the noun completarea?