Ion simply refers to an excess or deficiency of electronic charge such that an atom is no longer neutral. Atoms with less electrons than protons are positive ions, and atoms with more electrons than proton are negative ions.
Ions can form chemically, as in the example provided by mathman. In this case, the chlorine atom attracts electrons (it has a higher affinity for electrons than sodium) and thus the clorine atom attracts the electron from the Na atom, and we have a solution of Na+ and Cl-.
Ions can form by the photoelectric effect in which a photon of higher energy than the electron binding energy is absorbed by the electron which then escapes from the atom. But then the electron is likely to be attracted back to its parent atom, now an ions, attracts an electron from another atom.
Ions can also form by collision with other atoms. At very high temperatures, atoms become ionized, usually by collisions with energetic electrons or energetic atoms, and the result is a plasma or ionized gas.
