http://www.doubleddie.com/58243.html This site is very informative and has illustrations and information for overdates.
Here are two good examples of the mint creating overdates in its early years. In 1801, the Philly mint prepared dies for the 1801 Half Eagle, yet never coined any of that date during the year. As 1801 rolled in, the 1800-dated dies were still usable, and there were no doubt, a few thousand 1800-dated Half Eagles produced in the early months of 1801. Sometime during the year, focus turned to production of the 1801 Eagle... to the tune of of 44K coined... a large number, and a hefty sum of gold back in that day. Before long, 1802 rolled in, yet no 1801 Half Eagles had been produced. Die steel was very hard to come by, and the mint was reluctant to discard perfectly good dies. The answer was to take the 1801 dies and stamp a "2" over the "1", and viola... 1802/1 overdate. The mint also prepared regular 1802 dies for production later that year, but the 1802/1 dies managed to answer the year-long call. Before long, 1803 rolled in, and the solution was to stamp a "3" over the "2"... And so the birth of a consecutive overdate. 'dude