You eat food when you put it in your mouth, chew it and then swallow it. People generally cut their food up with a knife and fork before they eat it. You can also eat food with a spoon, chopsticks or your fingers.
You emerge from something when you come up out of it. The mouse in the picture is emerging from a play tunnel.
You engulf something when you swallow it up and take it over. The tree in the picture has engulfed the fence. You can also engulf yourself in something by becoming completely absorbed in it, for example "he engulfed himself in his new hobby".
Something gets eroded if it is being worn away. Mountains slowly erode over time and the rock they are made from turns to dirt. Erosion is only a problem if it happens too fast. When people cut down a lot of trees and plants all at the same time, there is nothing to hold the dirt together so it either gets blown away by the wind or washed away by rain. Once the soil has eroded away there is nothing to grow plants in for food, and the land becomes useless. The picture is of some bad erosion around a creek.
Something erupts when it throws something out with great force, for example when lava erupts from a volcano.
You escape from something when you break away from it, or out of it. People and animals most often try and escape captivity. The cat in the picture is escaping from inside a house.