An atom is the smallest, most basic unit of a chemical element. Atoms join together to make molecules, which join together to create matter (everything around us). However, the term is a misnomer, since "atoms" are composite.
The smallest atom is the hydrogen atom that in its neutral state consists of just one proton with an electron orbiting or creating a field round it. All elements heavier than hydrogen include at least one neutron (deuterium) or neutrons for anything heavier. Elements heavier than the different types of hydrogen include more protons and roughly equal numbers of neutrons. The number of protons in an atom determines which Chemical element it is. In their neutral state the number of electrons is exactly equal to the number of protons. Protons carry a positive charge which exactly balances the negative charge in the electron, therefore atoms with equal numbers of protons and electrons are electrically neutral. Sometimes especially when atoms are heated they can lose one or more of their electrons, then they are no longer electrically neutral, the free electrons are negatively charged and the nuclei are positively charged. Both parts of ionized matter react to magnetic fields in their area.
The illustration here is a common schematic of an atom. However, atoms more or less look like semitransparent fuzzy balls, as their nuclei do. That's because their electrons are standing waves that fade off with increasing distance from the nucleus. An atom's nucleus is as much as 100,000 times smaller than an atom itself, and it contains those protons and neutrons.
Electrons are waves as well as particles because of quantum mechanics. In fact, everything is both particle and wave, though on macroscopic scales, we see only particlelike or wavelike aspects.