In case you have saved pdf files in the document Library and another user wants to open, then SharePoint does not have the facility to open it in the browser. When you click on the link, it asks to save on the hard drive.
By using the PowerShell command, we can easily add the PDF MIME type to the web application's AllowedInlineDownloadMimeTypes property
$webApp = Get-SPWebApplication("http://abhay-pc:4444")
$webApp.AllowedInlineDownloadedMimeTypes.Add("application/pdf")
$webApp.Update()
As soon as you run the above code, and open the pdf, it shall open in the existing browser.