Strychnine has long been used as a rat poison (or other mammal/bird pest poison). During the 19th century production increased dramatically and it became practically a household item. Pest control has always been a major concern and in the early industrial age it was something many people took into their own hands.

Strychnine is an alkaloid so it has a quite bitter taste, which is an evolutionarily derived signal to avoid it. However, humans have acquired the habit of ingesting alkaloids such as caffeine (and theobromine in chocolate), quinine (a malaria treatment), nicotine, cocaine, and others, so we've overriden the natural instinct to avoid bitter flavors. This has made it possible for people to imbibe a lethal dose of strychnine without necessarily being immediately aware that they are doomed, and a lethal dose might be just a fraction of a gram. Indeed, there's the case of writer Henry Randolph who in 1892 mistook strychnine for quinine when mixing his tonic and accidentally killed himself.

Given strychnine's wide availability and the ease with which it could be used to kill someone it became used as a poison and, more so, became famous in literary tales in that role. Strychnine kills by causing convulsions which result in asphyxiation. One of the reasons it was a popular poison in the literature is because it's generally fairly obvious as a poison after the fact, leading to the classic scenario of a victim dying by poison with many potential suspects. As such things tend to do one generation of fictionalized portrayals of the use of strychnine as a poison gave rise to the next, and so forth. It developed into shorthand for "poison", everybody knew about it either from other media or from first hand knowledge of its use in pest control.