it is basically depend upon your SharePoint configuration, like which services are configiured on which server (apart from main Web Application) i.e UPA, Search service, Managed metadata service etc.
Web Front Server: Web Front End (WFE) servers form the connection point for clients that request content or services from SharePoint. Every request from a client is directed to a WFE server and every response to a client is sent from a WFE server. This means that all client requests place some load on WFE servers. A WFE server is responsible for:
- Processing incoming requests through IIS.
- Requesting any data from service applications and databases that are
required to service the request'
- Processing the data returned by service applications and databases.
- Compiling responses as ASP.NET pages and sending the responses to the
Application Server: By default, the server that hosts Central Administration in a three-tier farm is an Application Server. You can add Application Servers to host services that can be deployed to a single server and used by all the servers in a farm. Services means, User Profile Service, Search Service, Performance Point service etc.
Read more here: Understanding Server Roles in SharePoint 2013
If the app server is down than at least your central admin site will be down, But if you have configured the services application on the server then those will be down as well. But keep in mind, it is totally depend upon your configuration. in most orginzation they configured the service applications in a way if a server is down then from other server it can be accessible.
If you have 2 WFE then if one goes down, it will not bring down your web application but if both WFE are down then user will not be able to access the Web applications.
If Database server is down then whole farm will be down.
Now its depend upon the request, What type of action user are requesting. User need information from User profile or want to perform a search or simply getting the a page or upload a document etc. Wfe act as per the request, sometime it grab the information from local cache even not making a call to App or DB server. if information required from Managed Meta data service then make a call to app server then db (again depend upon on request) and serve the request.
its all depend how you design your farm topology and service configuration.