This is a breakout board for the very handy 16-Channel Analog/Digital Multiplexer/Demultiplexer CD74HC4067. This chip is like a rotary switch - it internally routes the common pin (COM in the schematic, SIG on the board) to one of 16 channel pins (CHANxx). It works with both digital and analog signals (the voltage can't be higher than VCC), and the connections function in either direction. To control it, connect 4 digital outputs to the chip's address select pins (S0-S3), and send it the binary address of the channel you want (see the datasheet for details). This allows you to connect up to 16 sensors to your system using only 5 pins.
More information is available on the website of Sparkfun.