The "Normalized Area" is the the peptide area normalized according to whatever normalization method has been specified in:
Settings > Peptide Settings > Quantification > Normalization Method

If the "Normalization Method" there is "None", then the normalized area is the same as the sum of all of the light precursors' "Total Area" values.

It looks like in your document you want to be using the "Ratio to Heavy" normalization method, which you can specify on the Quantification tab of the Peptide Settings dialog.

In Settings > Peptide Settings > Quantification > Normalization Method

What is the difference between "Equalize Medians" and "Ratio to Heavy"?

I have run a PRM experiment with spiked in heavy peptides and now I want to compare the proteins abudance. In order to do that, I need to choose one of the normalization methods but I am not sure which one fits better in my case.

Thanks in advance

With "Ratio to heavy", the normalized area of a peptide is calculated by dividing the area of the light transitions in that peptide by the area of the heavy transitions of that peptide.

When you have heavy and light transitions in your document, for the normalization method "Equalize Medians", Skyline figures out, for each replicate, which heavy transition has the median peak area. The normalization factor that Skyline divides by ends up being the median heavy peak area of the replicate divided by the median of the median heavy peak area of all of the replicates.

If you have only one peptide in your document then "Ratio to heavy" and "Equalize medians" will produce similar results, except that the Equalize median normalized value will have been multiplied by the median median peak area.
-- Nick