The last offeringpan-Hindu
Antyeshti means the last sacrifice, and the name carries the tradition's whole reading of it. A life is described as a sequence of offerings made into fire, beginning at the wedding when a household's fire is first established; the funeral is the final one, in which the body itself is offered. The rite is not framed as a disposal but as the completion of a series, which is why so much of its language echoes the wedding's.
Why the rites continue after the firepan-Hindu
The cremation does not end the obligations; it starts them. For the days that follow, and then at the ceremonies of the tenth, eleventh and thirteenth days, the family is understood to be doing something for the dead rather than about them — providing a body, joining them to the ancestors, releasing them onward. That is why a family with a death in it is busy for a fortnight, and why the fortnight matters to them.
Fire, and the households that do not use itsome traditions
Cremation is the form most Hindu communities keep, and it is what the classical rite describes. It is not universal: infants are buried in most traditions, renunciates are buried or immersed rather than burned, and some communities bury as a matter of course. A family whose practice is burial is not doing an incomplete version of this rite.