Proton
A proton is a positively charged particle in the nucleus of an atom; the number of protons determines which element the atom is.
Definition
A proton is a tiny particle with a positive charge that lives in the nucleus of an atom, and counting protons tells you which element you have. It carries a charge of $+1$ (exactly $+1.602 \times 10^{-19}\text{ C}$) and a mass of about $1$ atomic mass unit ($1.673 \times 10^{-27}\text{ kg}$), and the proton count is the atomic number that fixes an element's place on the periodic table. In a neutral atom the protons equal the electrons. Protons are baryons made of two up quarks and one down quark, they are stable when free, and in acid-base chemistry the hydrogen ion $H^+$ is nothing but a bare proton.
Example
Every hydrogen atom has exactly $1$ proton, every carbon atom has $6$, and any atom with $8$ protons must be oxygen. Sodium has $11$ protons, so a neutral sodium atom has $11$ electrons, and the ion $Na^+$ still has $11$ protons but only $10$ electrons. In the Bronsted-Lowry model an acid donates a proton, $HCl + H_2O \rightarrow H_3O^+ + Cl^-$, and the particle handed over is the entire nucleus of the hydrogen atom.
Key Insight
Protons are like an element's ID number: change the count and you have a different element. They never change in a chemical reaction, so when sodium becomes $Na^+$ it loses an electron, not a proton, and stays sodium. A proton is about $1836$ times more massive than an electron, which is why the nucleus dominates an atom's mass while the electrons dominate its size and chemistry.