Computers do not have any one particular purpose. Instead, they are a tool that is meant to serve human beings in any way that we can think of.
For example, we can use computers as a means of communication. We can use them to send email or to talk on Skype. We can use computers as a form of entertainment. We can watch movies on our computers or listen to music. We can play games on the computer as well. We can use computers for work. We can use them to help us do calculations or we can type documents on them.
Computers are very much of an all-purpose tool. They have no specific purpose but are, instead, something that can help us in many different ways.