What is a Power Inverter and which inverter do I need? What does a power inverter do?

For an awesome 200 Watt Portable auto Power Inverter InVert 200 only $44.99

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The list of questions below are addressed:

What is a Power Inverter? What are the uses of an Inverter? What type of inverter do I need? What are sine waves? How to calculate wattage from amperage and volts? Amps to watts conversion. What size inverter do I need? What can I power with an inverter? Inverters for CPAP? What is modified sine wave? What is pure sine wave? How does a sine wave work? What are sine waves? Inverters for multiple appliances. What is Peak Surge (surge current, inrush current)?