The security implications are that if the parameters to eval() are fetched from some third party (User input, Web Service, etc), you may be running someone elses code which may do something you don't expect.
Why is this important?
Imagine you are using some third party web service to enrich your user's experience, perhaps fetching information from facebook, and that web service gets hacked. Now the hacker can execute javascript code on your page, because you eval() some of the results from the web service, making the hacker able to inject anything in your DOM, infecting your users with trojans etc.
Now, if you hadn't used eval(), all that would have happened is that you'd have gotten bad data which you may have displayed or even, if you're a studious programmer, displayed an error message regarding the particular data.