Romanian is a Romance language spoken mainly in Romania and Moldova, as well as in some parts of Hungary, Serbia, Bulgaria and Ukraine. It is part of the Romance group of the Indoeuropean family of languages. It is easiest to learn if someone already knows a related language such as Spanish, Catalan, French, Galician, Portuguese or Italian.
The most closely related are the other Romance languages, Italian being the closest, but any knowledge of Spanish, French, Galician or Portuguese might be very useful, especially because of the lexical and vocabulary similarities and the grammatical structure. A bit of knowledge of the Latin grammar might be useful as well.
Even more distant Indo-European languages have many similarities in both grammar and even common words, as many languages, like English have borrowed extensively words from Latin.
It is useful to know the language if travelling in Romania, especially in rural areas. Many people who know English and Romanian will understand any of its relatives, especially Spanish, French or Italian.
Note that in Romanian, there is a formal and informal form when addressing people. The informal is tu (you - singular) and voi (also you - plural). Use tu when addressing friends or people you know well. When addressing strangers, use Dumneavoastră or vă. Dumneavoastră is used for stressed pronouns, which are optional, vă is used for non-stressed pronouns, which are mandatory for direct and indirect objects. For instance, Vă multumesc means "Thank you" (accusative case, direct object), and Vă dau un telefon means "I telephone (to) you" (dative case, indirect object) The formal form of address requires the second person plural form of the verb at all times, even when addressing a single person. (This is similar to the French construction, and, to an extent, German.) Using the singular form can be considered rude or even insulting.