Charge is just a property of matter. Charge is measured a lot of ways, but it always is a multiple of the charge of 1 electron (or proton; they’re the same, but opposite), which is called the elementary charge, or e. So, a simple way to measure it is to say a proton has a charge of 1e and an electron has a charge of -1e.
An atom with more protons than electrons will be positively charged, and an atom with more electrons will be negatively charged. If they balance out, it results in a charge of 0e.
The names positive and negative were initially just assigned arbitrarily and we keep them out of convention (even though it might actually have made some later discoveries a little more intuitive if they had been reversed, since a lot of electricity stuff deals with the movement of electrons). There’s nothing about the charges that makes them inherently “positive” or “negative,” they just needed opposite names.
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