The most important change is from non-charged to charged.
An atom can lose (or donate) an electron, so the positive charge in the nucleus is no longer balanced by the total negative charge of the electrons orbiting it.
Let's take sodium, which has a nucleus charge of 11+ and (as an atom) 11 electrons orbiting it, so the charges are in balance.
When it loses its outer electron, the charge of the sodium ion is
This is written as
The other way around can happen to e.g. a fluorine atom (nuclear charge 9+) that can gain an electron:
The behaviour of the ions is quite different from the non-ionized stuff. You wouldn't want to eat - or even touch - pure sodium, but we find sodium-ions in our table salt. The same goes for chlorine gas and the chloride-ions, that we also find in our table salt.
What stays the same:
The atomic mass. The loss or gain of an electron has no significant effect, since the mass of an electron is really small, compared to the mass of the nucleus and the original electrons.