The leaves of tomato seedlings – as well as many other vegetables and ornamentals - are riddled with tunnels.
The tunneling is caused by the immature stage, or larval stage, of a group of insects called leafminers, which for the most part are flies (Order Diptera). The tunnels are made as the larvae feed between the upper and lower surface of the leaf, meandering their way throughout the leaf. Sometimes, black thread-like strips of frass (insect droppings) can be seen in the tunnels.
In most cases, leafminer damage can be tolerated because of the several species of parasites (the good guys) which attack the larvae while they are feeding within the leaf tissue. Many times, damage is confined to seedlings. Once they are set out in the garden, the plants tend to outgrow the pest - while the parasites take over and keep damage to a minimum. Chemical sprays are generally not recommended because the larvae are well protected inside the leaf tissue. In addition, the spray would kill the parasites. Some people pick off the infested leaves and discard them. This may not be a good idea because inside those leaves many parasites are waiting to emerge to attack more leafminer larvae.