Always report effect sizes where possible. Effect sizes are measures of importance because they indicate how much effect the experimental manipulation had on the differences seen in the data. 

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The p value is the probability of the experiment having given the result it did purely by chance. 
The threshold of significance is almost always 0.05 so that if the probability of a chance outcome is less than 1 in 20, the experimental result is declared to be significant. There are other important thresholds as summarised in the following table

p value

Because the thresholds are conventionalised, we need to recognise the apparent arbitrariness of the conventions and not make such black and white interpretations.

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