HERE to see it on my custom historical markers map).
On February 2, 1848, the Treaty of Guadalupe Hidalgo was signed, formally ending the Mexican War. As part of the treaty, Texas was annexed to the United States (the war was fought over Texas to begin with, so annexation was the main result of the treaty).
When land is annexed, it must be surveyed in order to set the actual political border. This was easy for the majority of the southern borders of Texas, as they either bordered the Gulf of Mexico, or the Rio Grande. This became a little less clear north of El Paso, where the Rio Grande crossed into the New Mexico Territory.
Well, as luck would have it, the map used in the treaty was slightly flawed. Most importantly, El Paso was misplaced by 40 miles, and the Rio Grande was off by 2 degrees to the west. This resulted in New Mexico having a pretty valid complaint about its southern border.
Sooooo, John Bartlett was US Boundary Commissioner, and General Pedro Conde was the Mexican Boundary Commissioner, and they needed to do something about this new brewing dispute. On April 24, 1851, using astronomical observations, the two settled on the new New (enough news?) Mexico / Mexico border, which was located exactly (more or less) where this sign is now posted.
If you'd like to learn more, check out the following links: