A server is just that, a piece of (hardware or) software which serves content to the network. If you do not have a server, there is nothing which makes the app available, hence no webapp. So, you need server!
If you just want to make your webapp available, depending on the backend language, you have different options. There are a lot of hosters out there, which let you upload PHP and NodeJS applications. Also, a lot of cloud providers let you run a dedicated application, no need for OS management. However, you might need to get a virtual or even dedicated computer, which you have to configure yourself, if you cannot host your webapp backend any other way (for example if you are using a binary server application).