The list of things it does not mean is more useful than the definition, and it is what you actually need to read a result.
It does not mean the effect is large. With a big enough sample, a difference far too small to matter will be significant. This is the most common way significance misleads people.
It does not mean the effect is real. It means it would be uncommon under the no-effect assumption. Run twenty tests on nothing and one will typically come out significant - that is what the threshold means, arithmetically.
It does not mean the result will replicate.
It does not mean the study was well designed. Significance says nothing about whether the right thing was measured, whether the groups were comparable, or whether the analysis was chosen after looking at the data.
A non-significant result does not mean there is no effect. It frequently means the study was too small to detect one. Absence of evidence and evidence of absence are different, and reporting rarely distinguishes them.
So when you see the word, the useful next questions are: how large is the effect, how big was the sample, how many things did they test, and was this the comparison they planned to make.