What is the basic concept of positive and negative charge of an atom?
Sodium's proton number doesn't change else it'd become a different element. 

In basic terms, sodium donates an electron to chlorine's outer electron shell; there is no electron 'stealing'. As much as both ions' nuclei are surrounded by electrons, the charges of the ions are based on the ratio of protons to electrons. For example, in an atom, the number of protons and electrons are equal to give no overall charge. 

However, in an ion it's different; the sodium ion has 11 protons but only 10 electrons, so has a relative charge of 1+, as there's one more positive charge (proton) than there are negative charges (electrons). On the flip side, the chloride ion has 17 protons and 18 electrons, so has a relative charge of 1-, as there's one more negative charge than there are positive charges.

This then causes the electrostatic attraction between the two ions, which we call ionic bonding.