InDesign does not have this exact functionality. An InDesign document starts with a clean page. You can add any content you want. A page might have just one text frame with text flowing from page to page (like a Word document), it might have 100s of text frames in a large diagram or it might have no text frames and only graphics and images. To make a system of templates for such complexity seems like an impossible task.
InDesign does have something called Templates, but they are like ordinary InDesign files which just automatically makes a duplicate when opened so you don't overwrite the template file. Read more about templates here.
InDesign also has the concept of a Book which is a wrapper around a range of documents. In a way it can be used as you describe. One of the documents is chosen as the Style Source. When you edit styles, color swatches, master pages etc. in the style source, the other documents of the book can be synchronized to reflect the changes. Books are (obviously) mostly meant for creating books. Long documents which consists of a range of shorter documents. Read more about books here.
Besides that you can always load the styles of one document into another document manually.
For what it's worth, as a graphic designer I (perhaps surprisingly) seldom need a feature like this. Perhaps because I don't create content myself but almost exclusively receives finished texts and create layouts from that. When the layout is done, it's printed and delivered and that's that. I hardly ever have to go back and change older layouts to reflect changes in the styling of newer documents.
But I do see how templates could be helpful in theory. It's just really hard to imagine how changing styles globally wouldn't mess up all the documents. Remember that in InDesign you work with designed pages - not a never-ending roll of text like in word processors.
