I understand that if you’re talking about a whole atom, a positive charge means it has lost electrons and a negative charge means it has gained electrons. However, what does charge mean when you’re talking about a single electron or proton? What about it physically makes it positive or negative?
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I’m afraid there isn’t a good answer to this. The only real answer to “what is charge?” is “it is”. Electric charge is just a fundamental property of matter. An electron has a charge of -1, and that’s that. Protons aren’t elementary particles though, they have a charge of +1 because its constituent particles – 2 up quarks and 1 down quark – have charges of +2/3 and -1/3 respectively. Why do they have those charges? They just do.
For electrons, that’s just one of its inherent properties in our universe. Electrons are an elementary particle, they’re not made of anything smaller, they just are…
Protons, on the other hand, are made of 3 smaller particles known as quarks. The quarks are like the electron, they can’t be broken into smaller parts, and they have a fundamental charge. The sum of the charge of these 3 quarks are what give protons their positive charge.
The property of charge itself is one of a handful of fundamental properties of an elementary particle, we don’t know exactly what it is, only through its interaction with other particles.
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