Trigpoints are the common name for "triangulation pillars". These are concrete pillars, about 4' tall, which were used by the Ordnance Survey
in order to determine the exact shape of the country. They are generally located on the highest bit of ground in the area, so that there is a direct line of sight from one to the next. By sitting a theodolite (an accurate protractor built into a telescope) on the top of the pillar, accurate angles between pairs of nearby trigpoints could be measured. This process is called "triangulation".
A major project to map out the shape of Great Britain began in 1935. The network of triangulation pillars, with accurately known positions, led to the excellent OS maps which we enjoy today. The coordinate system used on these maps is known as the "National Grid", and it is essential that you are familiar with this system if you are to get the most of OS maps, or this website.