The brew group is the entire assembly that circulates the water to the coffee puck during the extraction. The brewing group includes only the components after the boiler. A brew group contains as a minimum the group head, and the portafilter, but sometimes has more components depending on the design, or the level of automation. Some brew groups are actively heated, some are passively heated by the boiler through contact. The entire brew group should be sufficiently heated in order to brew a proper espresso.
The most known brew group is FAEMA E61, designed in 1961 for semiautomatic espresso machines. The E61 revolutionized the espresso machine industry, their brew group was virtually in all of the commercial equipment for many years. Many of the commercial semiautomatic espresso machines still used the E61.
The brew group can be identified on an espresso machine as the protruding part on the front of the machine, complete with the portafilter once it has been locked into place. The group head is typically built heavy for heat retention and just a few inches above the drip tray, so that the espresso has minimal contact with the air when it is travelling from the group head and the coffee cup.
The brew group is where coffee extraction takes place and it is essential that it is working correctly and is regularly maintained as good espresso extraction is impossible without it.