An atom is the smallest discrete division of an element that can maintain the properties of that element.
The general idea of the atom is ancient. First proposed by the Greek philosopher Democritus in the fifth century BC, the word "atom" originally comes from the Greek "atomos" for "indivisible". Democritus' atom was lost in the centuries until it was rediscovered by Renaissance scholars translating Greek documents in their archives.
In 1803 John Dalton proposed the first serious theory of the atom supported by empirical research. In Dalton's model of the atom and its behavior: 1). the elements are made of tiny particles called atoms. 2). Atoms of a given element are identical. 3). The atoms of a given element are different from those of any other element. 4). Atoms of one element can combine with atoms of other elements to form compounds. A given compound always has the same relative numbers of types of atoms.
5). Atoms cannot be created, divided into smaller particles, nor destroyed in the chemical process. A chemical reaction simply changes the way atoms are grouped together.
Dalton's discoveries, while not widely accepted until some years later, turned out to be the foundations of chemistry as we know it today.
The next major advance in the understanding of the structure of the atom was made by Sir Joseph Thomson in 1897 when he discovered the electron. Prior to the discovery of the electron, the first sub-atomic particle, atoms were thought to be indivisible. Thomson was quite the genius. During a long and distinguished career, he discovered isotopes and invented the mass spectrometer.
In 1909 Thomson's student Ernest Rutherford discovered the decay of isotopes and made key discoveries about the structure of atoms by his famous "Gold-Foil" experiment demonstrating the phenomenon of particle scattering.
It 1913 it was Rutherford's student Niels Bohr that proposed what became known as the Bohr Model of atomic structure. In the Bohr Model, the atom had a small positively charged nucleus composed of positively charged protons and neutral neutrons surrounded by an electron shell. The stable (ground state) atom was in electrostatic equilibrium with its positively charged nucleus in balance with its negatively charged electron shell.
Although the Bohr model gave way the more sophisticated models of atomic structure of quantum mechanics, the Bohr Model of atomic structure is still taught to introductory chemistry students.