The µBoost is a battery powered USB power supply. It can supply up to 1A @ 5V from 3 primary cells (AA, C or D) or up to 500 mA from 2 primary cells.
You can use any supply voltage as long as it is lower than 5 volts. That means that you can use a LiPoly, NiCd, NiMh or any other chemistry you like.
Use of primary cells at more than 1A of current draw is not recommended. The batteries' internal resistance will cause them to get quite hot. Additionally, the higher the current draw, the less energy the batteries will deliver before they die (the extra energy is lost as heat). This is not a problem with most secondary battery chemistries, such as NiMh, Lion or LiPoly. If you wish, you can add a battery charger in parallel with the battery and µBoost.
The quiescent current of the converter (that is, its consumption with no load) is around 140 µA, which means that without being used, a set of AA batteries would last around 2 years.
The lower the input voltage, the hotter the MOSFET, diode and inductor will get during high current operation. It is not recommended to pull 1A with a 3 volt (2 battery) supply. Even if this weren't excessive switch current for the MOSFET, it would require pulling too much current from the primary cells than is good for them. If you heat up primary or secondary cells they can leak or explode.
Theory of operation
The µBoost is built around an NCP1450 boost converter controller with an external MOSFET switch. Because the switch is external, the controller itself has no limit on how much current it can switch (or supply). The MOSFET itself has a maximum drain current rating of a massive 8 amps, but in a boost converter arrangement the switching current is generally much higher than the output current rating. The same is true of the Schottky diode, which is rated at 3 amps and a maximum forward voltage drop of 0.5 V and the inductor, which is rated for over 2 amps.
A boost converter works because an inductor resists a change in the current flowing through it by generating a voltage. The inductor is connected between the line and load. Immediately after the inductor is a switch between the inductor's output and ground (in this case, the switch is the MOSFET). When the switch is closed, the inductor is connected across the input voltage, and it is effectively "charged." When the switch is opened, the current flow through the inductor is interrupted. The inductor attempts to "correct" this state of affairs by generating a high(er) voltage. That voltage passes through the diode to the load. When the switch is closed, the diode is reverse-biased and blocks current flow the "wrong" way from the load. The output filter capacitor supplies the load during this time.
The two data lines have resistor voltage dividers. These dividers are set to provide a constant voltage to the data pins. These voltages tell Apple iDevices the ampacity of the charger. The spec for these voltages is unpublished, but was discovered by the good folks at AdaFruit.
The only difference between the 500 mA circuit and the 1A circuit is the high side D+ resistors. It is 75k for 1A of charge current and 43k for 500 mA.