There are many types of server out of which some are explained in brief below.

Types Of Server
Application Servers
Application servers take up a large amount of computing area between database servers and the end user. This is used to establish connection between two database servers and end user.
A web server supplies static content to a web browser by loading a file from a disk and serving it across the network to a user’s web browser. The browser and server talking to each other using HTTP mediate this entire exchange.
FTP Servers
File Transfer Protocol makes it possible to move one or more files securely between computers while providing file security and organization as well as transfer control.
Microsoft Exchange Server is a messaging and collaborative software product developed by Microsoft. It is part of the Microsoft Servers line of server products and is widely used by enterprises using Microsoft infrastructure solutions. Exchange’s major features consist of electronic mail, calendaring, contacts and tasks, and support for the mobile and web-based access to information, as well as supporting data storage.
A database server is a computer program that provides database services to other computer programs or computers, as defined by the client-server model. The term may also refer to a computer dedicated to running such a program. Database management systems frequently provide database server functionality, and some Dumas’s (e.g. MySQL) rely exclusively on the client-server model for database access.
Real Time Communication Server
Four types of servers comprise our real-time communication category:
- Chat servers enable a large number of users to exchange information in an environment similar to an Internet newsgroups but with real-time discussion capabilities.
- IRC, or Internet Relay Chat servers, are a collection of server networks (or ‘nets’) that allow users to connect to each other via an IRC network.
- Instant messaging servers, like chat servers, facilitate communication in real time. However, while a chat room environment typically handles two or people involved in one or many discussions, instant messaging generally involves one conversation between two people.
- Instant messaging gateway servers act as the intermediary between consumer instant messaging networks and internal corporate networks. The server overlays IT management, compliance, and security features onto plain-text, unencrypted and anonymous public instant messaging clients.
TACACS server
A TACACS server provides a centralized location for Authentication, Authorization and accounting for Cisco devices. User authentication on Cisco devices can be done in one of 2 ways; via a local database of users on the device, or by a TACACS server.
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