A putty eraser is a soft, pliable eraser that can easily be shaped with your fingers and is used for erasing (removing) pencil, charcoal, pastel, and similar dry mediums from an artwork. Being pliable makes a putty eraser particularly useful for erasing small areas as you can shape it into a point. Various brands have different colors, from gray to off-white.
A putty eraser is gentler on the paper too as it's not as abrasive as a harder eraser. Particularly if you use it in a dabbing (up-and-down) motion rather than a side-ways rubbing motion. It means you're less likely to damage the surface of the paper if you do decide to erase something.
A putty eraser also doesn't leave annoying little crumbs over your artwork (which you then invariably brush onto the floor). Though be careful your putty eraser doesn't get tacky from heat or liquid (or old age), as then it may stick a bit on your paper.
Putty erasers definitely have a limited shelf life, though it's years, not months. Throw it away if it starts to get crumbly or lumpy, tacky, or hard, and buy a new one.
With use a putty eraser gradually becomes dirty as it accumulates graphite etc. When it gets to the stage it's depositing pencil on a sheet of paper rather than picking it up, it's time to replace it. (I have heard it'll wash clean if you put it in the pocket of a pair of jeans you then throw in the washing machine, but I've not tried it, so try it as your own risk!)
Finally, a putty eraser is also perfect for doodling sculptures, whether you're a bored art student or restlessly listening to a workshop talk. Mice, figures, hats, cars... wherever your imagination takes you, until you need to use it as an eraser again!
