In this paragraph the speaker describes his grandmother's look, who is living in a nursing home. He compares her with Ethel Barrymore and says they both have "faces like the side of a mountain and wonderful voices like syrup being poured". He means they both have rough-textured skins, like most elder people, and that they have soft silky voices.
The cartoonist is looking to reform the school system, if you look closely to the picture there is a public school outside of the "loop" and the private school is in the loop