SEER stands for "Seasonal Energy Efficiency Ratio". It's the ratio of total seasonal cooling output in BTUs to total seasonal energy input in watt-hours. (seasonal means its averaged to include part load conditions - it's not just a measure of performance at peak load)

So a 13 SEER AC unit removes 13 btus per watt-hour of energy input.

Payback will vary depending on electricity rates, unit size and cooling demand. As a very rough estimate, going from SEER 13 to SEER 16 might save you $200/year - a 4 year payback on your $800 investment. Keep in mind that a 4 year payback is equivalent to a 25% return on investment - lets see you do that in the stock market.

So go for the better unit. But don't forget that better insulation and windows will save you money too!