It means that there's a reason for a rumour. It is an analogy, as well as a proverb, as the rumour is likened to smoke and the underlying reason is likened to a fire.

It means there's a reason why something happened. For example: They broke up a year ago, but after some time they started to go out again together and they're thinking about a possibility, to be a couple again. - Well, I expected that because where there's a smoke, there's a fire.

In Ukrainian we say "Нема диму без вогню". I guess that has a link to a conservation law. Something cannot appear from nothing.