The difference between \citep and \citet is that \citet calls only one reference at a time whereas \citep can be given a list of references separated by commas. In addition, \citep allows a prefix and a suffix in the square brackets. This is useful for adding text like 'and references therein' or 'see also'.
In a document, you would cite something as follows:
This theory was first advanced by \citet{Smith86} but was later
disproven by several other research groups \citep[][and references therein]{Jones90,Brown92}.
...
\begin{thebibliography}{}
\bibitem[Smith et~al.(1986)]{Smith86}
Smith, G. S., Bang, R. T., Slosh, F. F., \& Dingle, Q. 1986, \apj, 299, 444
\bibitem[Jones(1990)]{Jones90}
Jones, X. Y. 1990, \baas, 188, 45
\bibitem[Brown \& Wakka(1992)]{Brown92}
Brown, T., \& Wakka, W. 1992, \apjl, 234, 45L
\end{thebibliography}
...
Smith, G. S., Bang, R. T., Slosh, F. F., & Dingle, Q. 1986, ApJ, 299, 444
Jones, X. Y. 1990, BAAS, 188, 45
Brown, T., & Wakka, W. 1992, ApJL, 234, 45L
Here is the code for a figure in its full glory:
\begin{figure}[t]
\epsscale{1}\plottwo{figs/lmc.ps}{figs/smc.ps}
\caption[LMC and SMC maps]{The LMC and SMC Galaxies as viewed in radio waves. Images courtesy \citet{Smith99}.}
\label{maps}
\end{figure}
In this example, two postscript files are being called. The first part of the caption is a short version which will appear in the List of Figures. The second part is a longer description which will accompany the figure.
When referring to this figure in the text, I could simply say Figure 3.2. But as soon as different figures are added, I must change the numbering. It is far easier to define a label by which the figure will be known. LaTeX keeps track of these things and will fill in the appropriate numbers in the right spaces. The \label{map} command defines the label. In the text, I would refer to Figure \ref{maps}. The same can be done with tables or sections of text as well.
In all cases, it is important to define the labels after the numbering has been established. The \label command must come after the \caption, the \section/subsection command, or the text of the table to have the correct number.