The two concepts are different, effect size estimates the impact on an intervention, significance idicates the likleyhood that the impact is due to chance or random effects.
You can have a very big effect, that is a fluke, or random variation, or you can have a very small effect size that is highly unlikly to be due to chance, and every thing in between.
In clinical work we like to have statistical significance (not due to chance) and clinical significance (the effect is big enough to be noticable and make a difference to a patient). A simple effect size calculation is to subtract the control (or before score) group overall score from the intervention group (or after score) overall score and divide by the standard deviation of the control group.
What is a good effect size? Depends a quite a few elements--but a rule of thumb is less than 0.5 small, up to 0.8 medium and over is large--but these are critisesed as being 'T shirt effect sizes'
Another important consideration is Confidence Intervals--these indicate the range of possible scores your result lies within