A tiller is an upright shoot that develops from nodes that are compressed in a specialized stem base structure (called a crown) of a plant. In corn, for example, these would be nodes 1-5.
A node is the region of plant stem where a leaf is attached, and also where buds form. They can be found by slicing the stem in half length-wise or by pulling the leaves (and sheaths) all the way back from the stem of a corn plant.
Tillers grow from axillary buds, which are found at every node on the corn plant. Not all plants have the ability to tiller, but some familiar crop examples are sorghum, wheat, and alfalfa (shown in photo).