That relates to when the flash fires. Lets take a long 1 second long exposure as an example. Slow1 "first curtain sync" will fire the flash as the exposure begins to be taken, in other words at the beginning of the 1 second. Slow2 is "second curtain sync" the flash fires at the end of the 1 second exposure.
Why?
Say you are taking a picyure of a fast moving fish and panning the camera during the exposure. With 1st curtain the result would be a fish "frozen" by the flash with a trail in front of it, which looks odd and unnatural. Usually you want the effect of having the trail behind the fish so that it looks like its moving fast, so you use second curtain sync so that you get a trail behind the fish and then a Frozen fish. Confused? Imagine this symbol is the fish ">" and "......" is the trail.
1st curtain sync would look like >....................
2nd curtain would look like ..............>
Basically unless you shoot slower than 1/8 or maybe slightly slower, they're won't be any noticeable effect (unless you pan the camera very fast)