objectives are the output of a research you attempt to find, the elements you hope to get and find once your study is finished in order to improve knowledge about the field of your research.
SIgnificance of a study is what you actually showed. High significance is when a study is particularly important for comprehending a phenomenon.
Another meaning of significance is statistical significance, which refers to the statistical criterion required to be met in order you can state that there was an effective effect of the experimental factors your manipulated.
"Another meaning of significance is statistical significance, which refers to the statistical criterion refquired to be me in order you can stating that there was an effective effect of the factors your manipulateur".
About statistical significance : depending on the field (for installe as in psychology, , cognitive neurosciences, medical sciences....), you need statistics when you compare data in two groups or more. Observing a difference in your sample is indeed not enough to admit that the difference can be applied to the refered population. Computing infernal statistics with help you deciding whether the effect you observe is really present. This is what is called statistical inference.
SIGNIFICANCE is how important are your results to beneficiaries of your research(in the exact field, whereas the OBJECTIVES: are the goals/aims of your study(why you carry out your research, what is the problem you addressed)