Authentication is a process by which UE and Network check if the other party has right authority to communicate each other. It is very similar to 'login process' when you use a computer. The only difference is that in computer login process, only the computer is checking your authority and you are not technically checking the PC's authority.
To improve this security issues, in LTE (in WCDMA as well) they do 'bi-directional' authentication, meaning that UE has to pass the authentication process and Newtork also has to pass the process as well.
http://www.sharetechnote.com/html/Handbook_LTE_Authentication.html