Why A triode has significant capacitance between the control grid and the plate, which feeds signal back from output to input (the Miller effect) and can make an RF amplifier oscillate. The screen grid is a mesh electrode placed between the control grid and plate, held at a steady DC potential and bypassed to ground for RF, so it acts as an electrostatic shield between the two. Adding it drops grid-to-plate capacitance from a few picofarads to a small fraction of a picofarad, which is why tetrodes and pentodes are the standard in RF amplifiers.
Watch out Gain and efficiency do improve as a side effect of the added screen, but the reason the electrode is there is shielding; the screen has no direct effect on control grid resistance, and plate resistance actually goes up, not down.
Screen grid = screening, an electrostatic shield that blocks grid-to-plate capacitance.