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Inside are two sensors, one is a classic 3-axis accelerometer, which can tell you which direction is down towards the Earth (by measuring gravity). The other is a magnetometer that can sense where the strongest magnetic force is coming from, generally used to detect magnetic north. By combining this data you can then orient your project!
Adafruit based this breakout on the latest version of this popular sensor, the LSM303DLHC. This compact sensor uses I2C to communicate and its very easy to use. Since it's a 3.3V max chip, they added circuitry to make it 5V-safe logic and power, for easy use with either 3 or 5V microcomtrollers. Simply connect VCC to +3-5V and ground to ground. Then read data from the I2C clock and data pins.