Diff between WFE,applicationserver,database server in Sharepoint

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WFE Role hosts sharepoint site and handle user requests,
Database Role hosts and manage Sharepoint databases,
Application Role can host some services like Excel, Forms ...etc

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WFE /Web Front end server serves the web sites to the users. These servers hosts the IIS applications and servers the pages.
Application Server is a server provisioned for serving applications like Infopath forms services, Excel services etc
Database server is the Server having Microsoft SQL server installed and holds the databases for sharepoint.

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The Web Front end Server is the server that is hosting IIS and serves the websites.
An Application Server  has services on it, for example, like Excel services, Project server, etc..
A database server simply hosts the SharePoint core db's and the other Content databases.. It just has SQL Server installation on it.

So you have to install Sharepoint to WFE's and App. Servers.. You dont need to install Sharepoint to the database servers on your farms.