To volunteer means to freely offer up your time and service to help. So a volunteer might offer to water a neighbor's plants while he's on vacation or sign up to serve dinner at a local homeless shelter.
When it came into usage circa 1600, the noun volunteer referred to a person who offered himself up for military service. It wasn't until a few decades later that the word was first used in a non-military sense. And a little over a hundred years after that, volunteer expanded from functioning as just a noun to also playing the role of verb. A volunteer is someone who volunteers: willingly performs a task or offers a service.