Bentching gomel is a special prayer that allows you to thank Hashem for delivering you from danger. (Imagine being at a football game..."Go, Mel!" It doesn't rhyme with camel.)
You must have actually been in danger. Close to danger isn't enough. You have defied death, so now you should thank Hashem in public during the Torah service. You recite it in front of a minyan, and they answer, "Amen, and may He who bestowed goodness on you continue to bestow goodness on you forever." This ceremony replaces the sacrifice that you would have brought in the times of the Beit HaMikdash.
Note: "Bentching" as a word will be dealt with separately next week.
There are traditionally four categories of events that give you the opportunity to bentch gomel. (It's called birkat hagomel in Hebrew.)
- Crossing a sea
- Crossing a desert
- Being released from imprisonment (always check your situation with your rabbi)
- Surviving a serious illness or injury
The desert and sea issues are particularly complicated with airplanes. You should check with your rabbi how your congregation deals with airplane trips. If they "count," you should bentch gomel for each leg of your trip.
Just to be clear: bentching gomel is totally optional. You haven't committed an aveira (sin) if you were in one of those situations and don't arrange to bentch gomel. However, you should "run to do a mitzvah," and this is such an easy mitzvah to fulfill, so why not do it!
Traditionally, illness included giving birth. Today, it's debated whether giving birth justifies bentching gomel since it is (thankfully) a very safe process today. However, if there were complications, you certainly could say it.
It is debated whether women can/should bentch gomel. While women were allowed to bring the sacrifice that bentching gomel replaces, Ashkenazim traditionally held that it was immodest for a woman to recite the prayer in front of the minyan of men required. Today, synagogues have split on this issue. Rav Moshe Feinstein (great rabbi generally accepted by most Americans) ruled that women could recite it, but that it should preferably be done in her husband's presence if she has a husband.
If you are a woman and "allowed" to bentch gomel, you will generally recite it from the women's section. Recite it loud enough so that at least ten Jewish men can hear you and respond. If you would rather your husband recite it on your behalf, you may certainly do that instead.