Alchemy was a protoscience in which people tried to turn lead (or any other metal) into gold, looked for the philosopher's stone and carried other more-or-less mystical activities.
At the time they thought there were 4 elements (earth, air, water, and fire), but now we know that those "elements" aren't really elements, and there are 90 something naturally occurring elements, from hydrogen to uranium. We need to be grateful to the alchemists because, with time, their protoscience became the science of chemistry.
The name goes back to antiquity, and it is likely derived from the ancient Egyptians' name for their land, keme: "black" land, as opposed to the red desert. In the Middle Ages, Arabs used their word for "the", al, with it, and the European borrowers of that word interpreted the "al" as part of the word. That has also happened with "algebra", "alembic", "algorithm", "Alcoran", and "Algeria". In the 1530's, Georg Agricola removed the "al" as part of his taste for purifying words, and it was only in the 18th century that the al-less version of the name ("chemistry") got used for the modern science instead of the ancient and medieval art. [1]
We should in no way criticize the alchemists for their ideas and practices, as they were doing the best they could with the information available to them. Eventually their ideas became more refined and chemistry gradually replaced alchemy.
It was however a long process. Already in the 14th Century Geoffrey Chaucer knew that alchemy fails [2] but the practice continued up to the 18th Century.
Before modern times, alchemical manufacture of gold may not have seemed very different from the numerous physical and chemical transformations that people could observe. Making metals from rocks. Salt dissolving in water. Burning leaving behind rock-powder-like ashes. Etc. Some people even got concerned about the consequences of success. Around 1370, King Henry IV of England outlawed "multiplying gold and silver", possibly being concerned about the value of holdings of those metals if they could be produced in large quantities. That was a serious potential problem, as the Spanish discovered in the sixteenth century. They ran big gold and silver mines in the New World, and they likely thought that it would make them rich. But it created a lot of inflation instead. "Everything in Spain is dear except silver", said a traveler in 1603.[3] Sir Robert Boyle got that law repealed in 1689 [4], possibly being concerned about a chilling effect on legitimate scientific research.
Obviously anybody practicing alchemy today would simply be ignoring scientific evidence and no serious scientist would now think of doing so. This can be nicely contrasted with religious ideas which masquerade as science. Old Earth Creationism is an example of how not to integrate scientific knowledge into one's world view. In fact, one could easily suggest they Old Earth Creationists should take a lesson from the alchemists and bring their views up to date.