If you entered the United States on a K-1 fiancé visa, and you are planning to make your home in the U.S., it is best not to plan on leaving again for the five months or more that it will likely take to get your U.S. residency (a green card).
A fiancé visa is good for only one entry into the U.S., so you can’t go out and come back on it.
If an emergency comes up before your marriage and you absolutely have to leave, try to make time to apply for a travel document (“Advance Parole”) at your local USCIS office, using Form I-131 (available for free download on the USCIS website). If you leave the U.S. without a travel document, the consulate may be able to revalidate your K-1 visa back in your home country, but it will take a hard look at your situation first. You could end up having to start over with a new fiancé visa petition.
There's also an exception ("automatic visa revalidation") for making short trips to the U.S.'s border countries, as described in, Can a Fiancé on a K-1 Visa Make a Quick Trip to Canada or Mexico?
In theory, once you have gotten married and turned in your application for adjustment of status (a green card) to U.S. Citizenship and Immigration Services (USCIS), any departure from the United States automatically cancels that application. USCIS will regard you as having abandoned your efforts. However, if you obtain special permission—called Advance Parole—the application will not be cancelled while you are away.
Obtaining Advance Parole is usually fairly easy, though not guaranteed. Most applicants for adjustment of status simply include the form for it—Form I-131—along with their adjustment application, whether they plan on traveling or not. You need not pay any extra fee to include this application with your adjustment packet.
Applicants who have spent any time in the United States without permission should not even think of using the Advance Parole option. Advance Parole only keeps your application alive while you are gone, it does not guarantee your reentry to the United States. Any time you ask to enter the United States, the border officer has a chance to keep you out if he or she determines you are inadmissible.
If, for example, you were late in filing for your green card by six months or more, the fact that you spent that amount of unlawful time in the United States could result in your being excluded for three or ten years. (For a review of penalties for unlawful stays in the United States, see Consequences of Unlawful Presence in the U.S.: Three- and Ten-Year Time Bars.)