Deborah,
The tear trough is basically the hollow area under the eye. It gets that name because it looks like it could be a gutter that tears would flow into from the eye. It is basically a deficiency of bony or soft tissue anatomy in the lower eyelid region that leads to a shadowing and tired appearing lower eyelid. Fillers are very effective to fill in this area as is autologous fat transfer. Fillers are the temporary solution and fat is long term or semi-permanent. Fillers are performed in the office and usually only have a little minor bruising an swelling. As little as 24-48 hrs of minor evidence of the procedure. Fat transfer is perfomed with sedation and requires a few weeks of down-time, but the results last years. Fillers for the lower eyelids last 9-12 months. Both are great options depending on your goals.
Ed Buckingham