A block of mass m travels in a horizontal circle against the wall...

The block moves in a horizontal circular path of radius $R$ with an instantaneous speed $v$.

The centripetal acceleration required for this circular motion is directed towards the center and has a magnitude of $a_c = \dfrac{v^2}{R}$.

This centripetal acceleration is provided entirely by the normal force $N$ exerted by the cylindrical wall on the block.

Applying Newton's second law in the radial direction gives:

$N = m a_c = \dfrac{mv^2}{R}$