Leaf miner is a term used to describe the larvae of many different species of insect which live in and eat the leaf tissue of plants. The vast majority of leaf-mining insects are moths (Lepidoptera), sawflies (Symphyta) and flies (Diptera), though some beetles and wasps also exhibit this behaviour. Like wood-boring beetles, leaf miners are protected from many predators and plant defences by feeding within the tissues of the leaves themselves, selectively eating only the layers that have the least amount of cellulose. The precise pattern formed by the feeding tunnel is very often diagnostic for which kind of insect is responsible, sometimes even to genus level. The mine often contains frass or droppings, and the pattern of frass deposition, mine shape and host plant identity is used to determine the species of leaf miner. A few mining insects utilise other parts of a plant, such as the surface of a fruit. Some patterns of leaf variegation are part of a defence strategy employed by plants to deceive adult leaf miners into thinking that the leaf has already been predated.
More details at: at http://rsnz.natlib.govt.nz/volume/rsnz_55/rsnz_55_00_003280.html
Photos below are of leaves damaged by leaf miners.
Thanks to Wikipedia for text and information: https://creativecommons.org/licenses/by-sa/3.0/