1st curtain sync means the flash will be fired at the beginning of the exposure, while 2nd curtain sync fires at the end of the exposure. 2nd curtain is useful when you want to create a trail behind a moving object, instead of in front.
I'll practice my laymans terms.
1st curtain sync means that the flash will flash just after the shutter opens, while 2nd curtain sync means that the flash will flash just before the shutter closes.