understanding JSESSIONID with basic authentication

I went through some resources about JSESSIONID. They say that HTTP and web-servers are stateless. Ok fine, I know this. But then they say- to add a state to these, sessions are used. And there is a session created JSESSIONID by web servers(in java applications). JSESSIONID helps web servers to recognize if the request is coming from the same previous user or a new user. But, this created a doubt in me:
For basic authentication(for example), we send username password with each request, along with JSESSIONID. So, what additional benefit does JSESSIONID adds to that request, if we still need to send credentials with each request. What is the benefit of remembering the client-requests(the idea of using session-cookies)?
Any real-world example, please.