A gigawatt is a real thing. It is a billion watts, which is the metric unit for energy conversion. According to the English rules of pronunciation, a G followed by an I is pronounced as a hard G, like “girl” or “gift” or “git to school and learn to talk American.” Most people are familiar with the unit of data storage known as a “gigabyte”.
However, “gigawatt” is not the word used by Dr. Emmett Brown in Back to the Future. In the movie, he states that the flux capacitor requires “1.21 jigawatts” to operate. With a J, since a soft G wouldn’t be appropriate there. When it means he is trapped in the past, Marty appropriately asks, “What the hell’s a jigawatt?” There is no such thing as a jigawatt. We have to assume it is a fictional quantity. Presumably, it is a jillion watts. Jillion is also a fictional word.
Edit: Oh, my. I stand more or less corrected. As suggested, here is the entry from Webster’s New Universal Unabridged Dictionary:
Online dictionaries, including webster.com, list both pronunciations. Some list the hard G as the primary pronunciation, others list it as the secondary. However, online dictionaries are somewhat suspect, as is any information found on the Internet. I should probably get my hands on a dictionary of American English. In any case, this may present somewhat of a professional quandary. What would my colleagues think if I started talking about jigabytes and jigabits?