HTTP Modules

HTTP module is an assembly which gets called for every request made to the application. You can use these to customize and extend ASP.NET request pipeline. HTTP Modules are similar to ISAPI filters in that they run for all requests.

ISAPI filter : Internet Server API (Read more here)

You can work on this example to see how HttpModule works.

Typical usage

• Security : because you can examine each request, your HTTP module can perform custom authentication or other security checks before the requested page, XML Web service or handler is called
• Statistics and logging: gather information in central place rather than on each page
• Custom headers or footers : Because you can modify the response you can inject content 

HTTP Modules differ from HTTP handlers. While module get called for all requests and responses, Handlers run only in response to specific requests.(MSDN)

HTTP handlers

This is the process which runs in response to a request made to an ASP.NET web application. More info.

Using IHttpHandler interface, you  can write custom HTTP handlers to process specific types of HTTP requests. It provides functionality much like ISAPI filters but in a more simpler way. 

The most common HTTP handler is ASP.NET page handler which processes your request for .aspx pages. 

Also see ihttphandler vs ihttpmodule

Resources

https://msdn.microsoft.com/en-us/library/ms178468(v=vs.85).aspx

MDSN - Introduction to HTTP handlers