'Promising' is a communicative function. It means 'making promises'. An example would be: 'Trust me. I won't tell anyone your secret.'

The only word that I can think of that you could simply replace "promising" with is "committing". "Examples of functions of the language include asking questions, requesting, conforming and committing." A promise is a commitment to do something but with the emphasis that it will be done. It won't be forgotten or ignored.

Thanks a lot.