First of all make sure that you have installed middleware software that came with your USB token or smart card.
Web eID is software that enables using USB tokens and Smart cards in web browsers for identification and signature creation purposes. It is developed and maintained by Estonian government.
The recommended way of installing Web eID is by installing the latest Open-EID ID-software package.
Other option is downloading Windows, MacOS or Linux installation package from https://installer.id.ee/media/web-eid/