Formal definition:
From the Greek legend of Hydra. When one head was cut off, Hydra grew another; this counter-intuitive result came from a well intentioned effort to fix the problem, but instead multiplied the problem.
How it applies
Software engineers may experience this problem when they "eliminate a monolith" and move to microservices. In fact, issues caused by the monolithic codebase may then return, or mutate to match the new structure.
Similarly, some management styles may try to silence dissent by removing individuals from a team; this may backfire and cause others to take note of the silencing act, further increasing dissent from the remaining members of the team.
Related
Streisand effect - efforts to censor information can lead to that same information being highlighted further, increasing awareness. This could be considered a specific variant of the Hydra effect.