What is sinewave and why is it important?
Power coming straight from the mains is Alternating Current (AC). This form of current alternates the amount of current flowing from the wall to the device connected. The other form of current is Direct Current (DC). This form of current provides the same amount of voltage at all times, so there is no wave to it, simply a flat line. Most computer power supplies will assume the computer will be plugged directly into the mains, so they expect to receive AC current. It then takes this AC current and converts it to the DC that the components of the computer need.
A more budget-friendly UPS will attempt to mimic the sinewave that comes straight from the mains by using a stepped sinewave. This looks like the steps on a staircase as the current increases and decreases. High-end UPSs can emulate a pure sinewave or sound almost identical to AC coming from the mains, or can completely mimic the power coming from the mains.
Why is this important? Well, most modern power supplies are far more efficient than models from the past. The main reason for this is that most use Active Power Field Correction (Active PFC). This guarantees that the power being sent to all of the components is being used efficiently. Devices that have Active PFC do not like being connected to a simulated sinewave UPS. This can cause stress and damage to the UPS and to the connected device. Whenever you use an Active PFC power supply, it is highly recommended that you connect it to a pure sinewave UPS.