Most of the time when New Relationship Energy (NRE) is mentioned, it's in the context of relationships (typically polyamorous relationships). The Poly Glossary on MoreThanTwo.com defines NRE as:

Last March, my partner Declan and I opened up our relationship. It was my first experience with ethical non-monogamy and I was both excited and scared. Would either of us get jealous? Would it work? Would we be able to handle it once it went from theoretical non-monogamy to one (or both) of us actually having additional partners?