Positive and negative charges attract each other I know that when two unlike charges brought near, they will attract and cancel out each other.
So my question is what does cancel each other means? Does they combine and form a neutral charge or negative and positive charges destroy each other or something unexpected happens.
 A: One possible meaning: If two objects are fixed in place, a short distance from each other, and they have equal and opposite charges, and if a third charged object is located at a much greater distance from either of them than the separation between them, then the sum of the electric forces that the third object feels from each of the first two will be close to zero.
Another meaning: If two electrically conductive objects with equal and opposite charges are allowed to touch each other, then a momentary current will flow between them until their charges are equalized. Since they started out equal and opposite, "equalized" means no net charge.
A third meaning: If a charged subatomic particle interacts with its own anti-particle, which by definition must have the opposite charge, then the two are anihilated: Both particles cease to exist, and two uncharged photons are created.
A: The phrase 'canceling out' can mean several things. One very reasonable interpretation is that if we define a system of two unlike charges of equal magnitudes, then no matter what their separation distance, the system's net charge$=0$.
So you can interpret the canceling out as summation of individual charges in any defined system, or net charge equaling to zero.
In our world,  protons carry a positive charge and a negative charge is carried by electrons. In a neutral atom, we have an equal number of protons and electrons, and so if we define the atom as a system, the system has zero net charges. In other words, equal protons and electrons nullify each other's properties.
Now we do observe phenomena known as radioactive decay (in many different forms). In K-capture decay, the innermost electron is captured into the nucleus and combined with a proton to form a neutron. But this is a radioactive process and is observed in the radioactive nuclei only.
