This is a Hebrew term which literally means The Blessing (Birchat, same root as Bracha) on the Food (HaMazon). Would more usually be translated as "Grace after Meals". Is often referred to as "Bensching".
There are three different blessings that Religious Jews say after a meal, depending on what they have eaten. It is a commandment from the Torah to bless - "V'alchatah, V'savachta, Ov'rachta" - "You shall eat, You shall be satisfied and You shall bless" (Deuteronomy 8:10). The first two are short, and not usually referred to as Birchat HaMazon, but I'll deal with them briefly.
This is a short blessing which is essentially said when you haven't eaten any foods for which you need to recite one of the longer blessings! It translates very simply as
Blessed are You, Oh Lord our G-D, King of the Universe, who creates numerous living things, with their faults, for all that you have created, with which to maintain the life of every being. Blessed is He, the life of the worlds.
This would be said after eating a sweet or a bar of chocolate for example.
The "Three Faceted Blessing"
This is a longer blessing which is said if you have had a food from one of these three groups.
- After drinking wine.
- After eating fruit that was traditionally produce of Israel - grapes, figs, pomegrantes, olives or dates.
- After eating grain produce, except for bread or matzoh - such as biscuits.
This is a longer blessing, in which G-D is praised for making the food, and for giving us the land on which go grow it. It then asks G-D to rebuild the Temple in Jerusalem, and to let us be satisfied with the produce of the land.
Full Birchat HaMazon
This is the full Grace after Meals, which is said after eating a meal that was started with bread. This is because in ancient times, all proper meals would have bread. Nowdays, it is accepted that if you have a full meal, even if doesn't include bread, this is the appropriate way to finish. This covers all the food you eat. Often at a family Shabbat or Yom Tov meal, the whole thing is sang together.
It consists of a number of sections.
- Introductory Psalm: On Shabbat or Yom Tov, Psalm 126 is said first. On other days, some people have the custom to say Psalm 137.
- Formal Invitation: If three or more men are saying the Birchat HaMazon together, a formal Invitation to bless G-D together. One is appointed the leader - often this will be a Cohen if one is present. There are special enhanced introductions for the meal after a Wedding and at a Brit Milah.
- First blessing - for the nourishment: The first blessing was composed by Moses primarily as thanks for the Manna that fell from Heaven while the Children of Israel were in the desert.
- Second blessing - for the land: This was formulated by Joshua and is a blessing of thanks - "for the land and for the food".
- Third blessing - for Jerusalem: This blessing was composed by King David and King Solomon. It asks G-D to return Jerusalem to its former glory.
- Prayers for the day: At this point, a prayer is inserted if the day is Shabbat or Yom Tov.
- Fourth blessing - G-D's goodness: This blessing was composed by a Rabbi to praise G-D directly.
- Praises: Following this are various verses of praise - starting by praising G-D, and then various verses that are said by different people. A man in his own house asks G-D to bless him, his wife and his children. A child at his parents table (and this applies to an adult child as well) asks G-D to bless his parents. A guest asks G-D to bless his host.
- Supplications: If the day is Shabbat or Yom Tov, extra supplications are inserted here - for example, on the first day of a (Jewish) month, "May G-D inaugurate this month upon us for goodness and for blessing". There is also an extended section here at a Brit Milah.
- Closing verses: Related to those who are good being satisfied with their lot from G-D.
After this, at a wedding meal, the Sheva Brachot are recited.
The full Birchat HaMazon is long, and if sung, takes 5-10 minutes. There are a wide variety of tunes, some of which are almost universal and some passages have various tunes. On the other hand, someone reciting it after a weekday meal would probably take no more than 2-3 minutes.
There is also a shorter form, which contains the key parts of the blessings, that can be used if time is honestly very short (eg a medical emergency or a time of war).