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If we plot for example the relation between the probability of False Alarm (pfa) and the threshold. The threshold is in x-axix, while the $log _{10}(pfa)$ in y-axis.

If I get for example the following plot:

enter image description here

Which is better? the green one or the yellow one? Thank you if you can give me some explanations.

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Just read the graph carefully. With a low value threshold, you have a very high log probability of false detection. You want to minimize this detection rate. If your goal is to minimize the false alarm rate with a lower threshold, then the yellow curve is preferable. The false alarm rate drops off at a lower threshold in that case, and more rapidly too. Stated another way, you will get fewer false detections over a wider range of thresholds with yellow.

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