WhatsApp Web on a computer allows you to view all of the chats that are on your phone on the computer, including media. Once chats are synced you can view them offline, and you can download media to the computer from it. You can use it to send/receive messages, but only while your phone is online and connected (you don't need to open WhatsApp on your phone).
So if you just wish to view messages on a computer it's fine. It doesn't provide a way of exporting a chat into some different app (which app would you want to import it to?), though you can copy text and download media from a chat individually. It doesn't download all media from a synced chat automatically - if you look at recent messages the images will be there, but if you scroll back to old ones you will have to reload them. So it can probably do what you want, insofar as I know what exactly you have in mind, but if you are wanting to copy the chats to something else or download the media for viewing in another app you'll probably have to do it message-by-message.