It's short for E-Money Institution or Electronic Money Institution. It's a non-bank deposit taking institution. The term is most often used to refer to financial institution licensed as e-money institutions within the EU/EEA, under the E-Money Directive (2009/110/EC) and Payment Services Directive 2 (2015/2366).
However, it's used loosely enough now to also include non-bank deposit taking institutions outside of the EU.