Most of the web applications require Digital Signing documents, files, eReturns (XML or JSON) etc, from the user's browser using the user's local machine keystore, USB token or smartcard. Older methods being Java applets, Active X, etc. which are phased out or are being phased out from the new modern browser offerings.
Recently much is being talked about WebCrypto API but as of now, WebCrypto API does not provide access to Windows' or any other keystores or a local crypto USB/smartcard device.
June 2021 Update
Signer.Digital Browser Extension Host Version 1.7.0 now offers better user control to enhance security by asking user about Allowed Origin (website) which is trying to access certificates/keys. Also this version has Auto Update feature so that user automatically gets any security updates/enhancements after approving update by User Account Control dialog.