Clients don't have profiles, but you can access some of their information before applying to a job. To do that click on a job post and on the right column, under the button "Submit a Proposal" you will see it reads "About the client" where you can check country, time zone, how much they spent so far, average rate paid, etc. Below the job post you will also see the "Client's recent history" where you can see past jobs by that client, how he/she was rated and how he/she rated other freelancers. If the client is brand new you will not see information at all, maybe location only.
If you want to see the information about a client you are currently working for you will need to access the original post you applied to. To do that go to "My Jobs", click on the contract you are working, then Terms & Settings and on the right column you will see "View original job posting."