The biggest risk here is that you put your foot in something sensitive and handle it badly. Never make assumptions about what another person is feeling; ask first. Then address the problem directly, as it relates to the job. If, for example, the person is feeling a lack of confidence, a simple pep talk may help; show the employee that they have done well in the past, and give objective reasons as to why you feel that you can have faith in them.

If, on the other hand, the person is dealing with some serious personal issue, focus exclusively on how it impacts work and how you can help get the work done (assuming that there's not a case for giving the employee some time off while other team-members cover the work). Don't try to offer life advice; the odds that you're even remotely qualified are almost nil, and the risk of doing some real damage is high. Hand this one off to the HR department, or tell the person about your organization's Employee Assistance Program (EAP), if it has one...