I know browsers store session ids using cookies and check these ids on each request. My question is the following: when you make a REST call from your mobile device (or any other device), how does the client-server communication identify sessions and assign unique session ids to each client?
It is not clear wether your question is related to what actually happens to the client side or to the server side.
From the (java) web server point of view, a sessionID is just an id, and there are basically 3 ways to communicate with a client and to deal with this ID (so the server knows with which user it is talking with).
The usage of cookies is not strictly limited to the usage of a web browser as the clientm as any client can put cookies in the HTTP header.
If you want to know how a specific client can deal with the server to communicate session information, please be specific about what client you intent to use, because the implementation details (and therefore client code) may vary, even if the general mechanism is identical.