DOP stands for Dilution of precision. Basically, DOP is a measure of the effect of the satellite geometry on the error of the position computed by your GPS receiver. A simple example of DOP for a two-dimensional case is shown below:
A simple DOP example

This example is taken from R. Langley. The figure shows the case of two transmitters. The dark red and green line is the "true" range. If there was no uncertainty, or error in the measurements, the receiver would be located exactly at the intersection while the faded lines show the uncertainty of the range measurement. The effect of geometry is represented by the area highlighted in red. For the good geometry of the left,the area is quite small, but for the poor geometry case (on the right) the area is expanded.

If we have a reasonable estimate of the measurement uncertainty, then multiplying the uncertainty by the DOP will provide a reliable estimate of the position error. But if there are systematic errors, for example caused by the atmosphere, errors in the satellite orbits or multipath, then the relation between DOP and position error quickly breaks down.

There are many kinds of DOP: VDOP(vertical), PDOP(position), HDOP(horizontal), GDOP(position+time) and TDOP(time). As DOP can be an important factor for high accuracy users, most surveying softwares provide DOP simulation tools to view how DOP changes over time. DOP can be simulated for locations and times which makes it good for planning purposes. Here is an example of one online tool available to the public here.

Trimble online GNSS Planning Tool

What is DOP good for?

In the past DOP was an important factor for planning surveys. Before there was a full constellation of 30+ GPS satellites choosing the time of day to perform surveys was crucial. Using Trimble's Online Planning tool we can see the effect of a smaller constellation has on the user's DOP. Below the DOP plot we can see the number of satellites visible to the user and how this relates to the DOP.

DOP for a constellation of 20 satellites

Number of satellites visible

DOP was also important before the development of all-in-view tracking receivers. In the early days of GPS receivers could potentially only track a handful of satellites at a given time. DOP could be used to determine the optimal satellites to use in the position solution. Nowadays with some receivers having well over 200 channels for tracking this is no longer an issue.

This being said, DOP can still be an important factor for surveys requiring high accuracy. If you are working in areas that have obstructions near the horizon, or if the satellites gods are out to get you it is possible to end up with large DOP values, so using planning tools can still prevent down time. Additionally, since the GPS constellation just about repeats itself 4 minutes earlier each day, once you look up your location once, you are good to go for a long time.