A panel survey is a kind of longitudinal study.
In effect the survey sample (known as the panel) is asked repeated questions over time. This allows the measurement of change over time for the units of analysis.
For example you could measure unemployment by taking a random sample of the working age population and asking them whether they are working or looking for work. Later you could take a different random sample, and get a new number at the later date. This would be a series of cross-sectional studies and could give you an estimate of the net change.
With a panel survey, you could ask the same people at different times, giving you an estimate of gross employment flows and other more interesting details of change over time. The difficulty is that some members of the panel might leave, and if this departure was related to the question of interest then it could bias the results. In addition, even if the panel was typical at the start, it might cease to be in future simply because all its members had become older.