>What we are incrementing with a value of one.

You are incrementing the parameter `run` which is a public/global and special variable for LTspice's internal use.

>Is this something like in the 1st iteration we take resistor value as R = R+Tolerance and in 2nd it is like R-Tolerance, something like that?

No. `mc()` function is something like a random generator between the given boundaries with a uniform distribution. In your circuit, at each iteration, each resistor will have a random value within the range set by their minimum possible and maximum possible values (i.e. in \$[R(1-tolb), R(1+tolb)]\$ range). And this function takes the parameter `run` (as stated before, a special variable for LTspice, just like `time`) as input, so you need to manually increment it at reach iteration so that the random generator doesn't generate the same value. That is what `.step param` function does.