The first icon in the first row, which looks like a layer with a blue light bulb icon, is for the layer off command. This tool will let you turn off a layer by selecting any object of that layer from the drawing area:

To use this tool, select it from the Layers panel or use its command alias, LAYOFF, and then click on an object from the drawing area. The layer of your selected object will turn off and all the objects on that layer will disappear from the drawing too. You can select multiple objects from the drawing area too, and as soon as you click on an object, the layer of that object will turn off.

To turn all layers on, click on the icon that looks like three layers with a yellow light bulb right underneath the layer off icon in the second row of the Layers panel. As soon as you click on the icon, all the layers will turn on and all objects on the respective layers will also start to show up.