A shuttle is a device used in weaving to carry the woof (weft) yarn or thread back and forth between the warp threads. The key phrase here is back and forth. The more widely understood definition today, that of a) Regular travel back and forth over an established, often short route by a vehicle, or b) A vehicle used in such travel: took the shuttle across town, derives directly from the name of this textile tool.
Below are pictured of a simple stick shuttle, the older variety, and the newer (invented in the 18th century) fly shuttle (or boat shuttle). Many other variations exist, but these are the two basic types.