The noun plague [ˈpleɪ̯ɡ] in English has two major senses. On one hand, it can refer to ‘a sudden destructive influx or injurious outbreak’ or ‘a widespread affliction or calamity, especially one seen as divine retribution’, such as a plague of locusts or a plague of accidents (AHD). Secondly, the noun plague can refer to ‘a highly infectious, usually fatal, epidemic disease; a pestilence’, in particular one ‘that is caused by the bacterium Yersinia […] pestis, is transmitted primarily by the bite of a rat flea, and occurs in bubonic, pneumonic, and septicemic forms’ (AHD). The second one of these meanings is the one we are interested in here since it refers to the infection and disease. The Spanish cognate plaga, on the other hand, only has the former of these two meanings, however, not the medical one. The medical sense of Eng. plague is expressed by Sp. peste, a cognate of Eng. pest.
The word plague, borrowed from Old French around the year 1400, comes from Late Latin plāga ‘blow, stroke, wound’, which comes from the Doric dialect of Greek πλᾱγά (plága), cf. Attic Greek πληγή (plēgḗ) ‘stroke, blow’, from a verb meaning ‘to strike’, such as πλήσσειν (plḗssein). The word is probably related to root plag- of Lat. plangĕre ‘to strike, lament (by striking the breast)’ (cf. Sp. plañir). The Vulgate (original Latin translation of the Bible) uses the word plaga with the Biblical meaning ‘plague, pestilence, etc.’ (For more on the words Eng. plague ~ Sp. plaga, see Chapter 41, §41.7.)
The disease known as (the) plague, caused by the bacterium Yersinia pestis (earlier known as Passarella pestis) found in fleas and carried by ground rodents, is quite rare today, with under a thousand human cases reported each year. The mortality rate is high, however: 70% for those without treatment with antibiotics and 10% for those treated. However, this disease is famous for large outbreaks in pre-modern times in Eurasia, including the 14th century pandemic known as the Black Death, the Great Plague, or sometimes the Black Plague (Sp. peste bubónica), one of the most devastating pandemics we know of, which killed probably 100 million people (estimates vary from 75 to 200 million people) or at least one third of the population (more in some places than in others). Nowadays, there is also currently a vaccine for the plague bacterium.
As mentioned earlier, three types of plague are distinguished, depending on how it is transmitted and expressed: bubonic plague, septicemic plague, pneumonic plague (Sp. peste bubónica, peste septicémica, and peste neumónica). In bubonic plague, after the flea bites the host, the bacteria spreads through the lymphatic system and the swollen lymph nodes form the characteristic buboes associated with this disease (hence its name). The word bubo (pl. buboes; Sp. bubón) comes from Late Latin būbō (gen. būbōnis), from βουβών (boubṓn), meaning ‘groin, abdomen’ and ‘bubo in the groin’, which refers to ‘an inflamed, tender swelling of a lymph node, especially in the area of the armpit or groin’ (AHD).
Septicemic plague happens when the toxins made by the bacterium spread through the blood, causing tiny clots throughout the body, which may result in ischemic necrosis (tissue death). Finally, pneumonic plague arises from infection of the lungs. The coughing and sneezing of those infected with pneumonic plague is highly contagious.
Finally, let us say something about the cognates Eng. pest ~ Sp. peste, since the latter is the Spanish word for this disease. The words come from Lat. pĕstis ‘a deadly, esp. an infectious or contagious disease, a plague, pest, pestilence; also, a noxious atmosphere, unhealthy weather’ and, by extension, ‘destruction, ruin, death’ (L&S) (gen.: pĕstis; acc. pĕstem). It is possible that this word is related to the third conjugation verb pĕrdĕre ‘to destroy, ruin; to suffer loss’, the source of Sp. perder ‘to lose’ (principal parts: pĕrdō, pĕrdĕre, pĕrdĭdī, pĕrditum). This verb is derived from the verb dāre ‘to give’ (source of Sp. dar) by the addition of the prefix per‑ ‘through’. The Latin adjective perditus, derived from this verb’s passive participle was used with the meaning ‘destroyed, ruined; wasted; lost’.
Eng. pest [ˈpɛst] was borrowed from French peste in the mid-16th century with the meaning ‘pest, pestilence’, in particular with reference to the bubonic plague. (French itself had borrowed the Latin word pĕstis less than a hundred years earlier.) However, that meaning of the word is now archaic and the main meaning of Eng. pest is ‘a destructive insect or other animal that attacks crops, food, or livestock’ (COED) and, informally, ‘an annoying person or thing’, especially a child. Spanish peste is also first attested in the first half of the 16th century, so it was probably also borrowed through French, just like Eng. pest. Sp. peste can mean ‘plague’ but it can also have the same sense ‘bothersome thing’ as Eng. pest in some contexts, as in ser la peste ‘to be a big nuisance’. The most common meaning of the word, however, is probably ‘stink, stench’, used in colloquial speech, as in peste a tabaco ‘tobacco stench’. A well-known expression that involves this word is decir/echar/hablar pestes de alguien ‘to run somebody down’. Finally, in the southern cone, peste is sometimes used for an infectious disease, in particular smallpox (Sp. viruela) and in the Andean region is also used for the common cold (Sp. resfriado).
 The whole thing may have started as part of biological warfare by the Mongols in the Crimean peninsula. Note that the Japanese Army also weaponized the plague during World War II and used it against Chinese, Korean and Manchurian civilians and prisoners of war.
 The only English word containing this root is perdition which, in Christian theology refers to ‘a state of eternal damnation into which a sinful and unrepentant person passes after death’ (COED). It comes from Late Latin perditiōnem (nominative perditio) ‘ruin, destruction’, derived from this verb’s passive participle stem perdit‑.