In asking this I can safely assume that you have at least a rudimentary understanding of the workings of a computer.
Serial ATA (more commonly referred to as SATA, or the newer SATA2 standard) is a new standard connection for computer storage devices such as hard drives and DVD drives, that replaces the older IDE system of connection.
SATA holds a few advantages over IDE, the first and most important of which is speed. SATA devices have a faster data transfer rate than IDE had. SATA 2 is twice as fast as SATA.
SATA devices use a new connection method. Gone are the old IDE Ribbon cables, and molex plugs, SATA now has some much thinner and smaller data and power cables. Because the plugs are physically a lot smaller, it means more sockets for SATA data points can be fitted onto a motherboard.
Because the cabling is much simpler going straight from the motherboard to the drive, the need to set individual drives to be slave or master drive has gone, which means no more messing with small fiddly jumpers!
One of the great benefits is that SATA devices ate "hot swappable", which means even if a drive is powered up, it can still be unplugged and removed, and you can plug SATA drives into powered up systems with no adverse effects. This is great if you run multiple drives in an array or raid.
Finally the cost is usually cheaper than a comparable IDE device these days.