Bentch (pronounced like and sometimes written as "bench") is the Yiddish word for "pray." It's a verb. "Bentching" is the noun. "Davening" is the Yiddish word normally used for praying, but bentching is still used for very particular kinds of davening. You can "daven" anything, but you only "bentch" a few particular things. It doesn't make any sense to a native English speaker, so just memorize its uses.
Let's discuss these phrases in turn:
- Bentching: The grace after meals, birkat hamazon. You bentch from a bentcher, those little books on the table that are probably in a napkin holder. If "bentch" is used by itself, the person is talking about this bentching.
- Bentch gomel: A prayer said during a Torah service when someone survives a life-threatening event. See Phrase of the Day: Bentching Gomel.
- Bentch licht: Lighting Shabbat candles. This is the least-used of the phrases.
UPDATE: The commenters have added a couple of uses and clarified that bentch generally means "bless," so it is used when making brachot (blessings). These are the additions:
- Bentch the kids. This is when parents bless their children on Friday nights soon after Shabbat starts.
- Bentch lulav. This is the blessing over the lulav during Sukkot. We'll return to this in greater detail in just a few short weeks. The lulav is perhaps the craziest-appearing thing that Jews do.
- I also suggest that you read the Curmudgeonly Israeli Giyoret's use of bentch in the first comment below. It's hilarious.
Used in context:
- It's time to bentch.
- Should married women bentch gomel or should their husband bentch it for them? (An actual halachic maklokes)
- Have you bentched yet?
- Give her a second, she's bentching.
- It's almost time to bentch licht.