A family of Microsoft word processing software products for creating web, email, and print documents.
As the other person correctly explained, very old versions of Office did not require a Microsoft account. The modern version - Microsoft 365 - is a feature of a Microsoft account. (Your old version of Office won't install on a phone.)
Since you obviously have a Microsoft account, you can sign in to modern Microsoft 365 on your phone with your Microsoft account username and password.
Keep in mind that everyone is able to use the online version of Microsoft 365 on the internet and on a phone for free. The online version does not have the advanced functions of the desktop apps, and all your documents will be saved to your OneDrive, but that works perfectly fine for many.