It just means that they have looked at some other potential causes of the effect they are seeing and have concluded that they wouldn’t explain it. For example, if you are studying which fertilizer works best, you might compare yields from farms that have used different fertilizers, but you’ll want to check that those farms are otherwise similar – if it turns out that the low-yield farms all had low rainfall, that might be a better explanation. Ideally your analysis would take into account differences in rainfall by, for example, only comparing farms that had similar rainfall.
Clearly it’s never possible to rule out *all* other potential explanations. In my experience this is one area where it’s particularly common for researchers (and certainly secondary sources such as press releases and media articles) to exaggerate the findings slightly by being overly dismissive of alternative explanations. I’m not sure there is really ever a context where it would be appropriate to use the phrase “we’ve controlled for all other variables”.
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