It refers to an initiative taken by more than one country but not many, and not by a supranational political grouping or range of countries in a region - such as the European Union - to set up a programme focussed on e-learning in university-level institutions.
If the initiative involves a supranational political grouping or range of countries in a region it is not classified as an multinational iniatiative but as an international initiative.
If the initiative involves just one country or a region within that country then it is called a national initiative.
Very often the multinational initiative will set up a consortium or generate a newly created institution of a unique nature in the nations involved. This leads to some overlap of the UNESCO classifications.