I think you are confusing formal charge, overall charge of a compound, and overall charge in solution.
The formal charge of Mn in permanganate is +7. The overall charge on permanganate is -1. The +3 refers to the overall charge of the left side of that reaction, the combination of the charges of permanganate and hydrogen. When the charge of the hydrogens (+4) and the charge of permangante (-1) are added together we get an overall charge +3 for everything on the left side. Now the right side of that half-reaction reaction has an overall charge of 0 and we need the overall charges of the left side to equal the right side. That means we need to somehow add something to the left side that can account for a charge of -3 . The way we can do this is by adding 3 electrons since each electron contributes a -1 charge.