Can somebody explain these tax breaks?

You are for the most part correct Rey.  Those are federal tax breaks, and Puerto Rican residents earning  income from island sources do not pay federal taxes.  However, all of those with federal jobs do pay federal taxes.  I don't know what proportion of the workforce has federal jobs, but it's only about 2% nationwide.

I just don't get why the big push for it when it is applicable only to 1-2% of the island population. It is all over the PR newspapers like it was of great benefit to the people in general.
Here is one http://www.elnuevodia.com/english/engli … s-2267982/

Thanks for the article.  The proposal from Sen Hatch is not clearly described.  It may be that he is proposing extending the tax credit to Puerto Ricans even though they do not pay federal income tax.  Since this is a tax credit, I don't know how this would work for those who do not file federal taxes.  Perhaps some sort of direct payment? The article also seems to indicate extending Medicare subsidies.

It seems that Hatch (and I guess the Senate Committee on Finance) want to see the economy of Puerto Rico improve, but not see the Puerto Rican government continue to spend money it doesn't have.  This means finding ways to put more money in the pockets of Puerto Ricans, without directly subsidizing the Puerto Rican government.

One thing the goverment can do is make it easy and quick to get all sorts of permits for construction and for starting businesses.
In PR we tend to spend any money we get which fuels the economy, however a smart person would save instead and let others spend every dime.
We need more people to create businesses and as such create jobs, above board means more taxes for Hacienda, grey market jobs cause money that goes directly into the economy but little to none for Hacienda.
PR goverment needs to take lessons from successful states, where state taxes are around 5-7%. Or go with property taxes like NH. They need to learn to live on a budget that depends only on a 5-7% state income tax. Today the income tax is around 15-37% depending on income level. Today's income tax combined with Federal would raise taxation into 40-60%, which will never do. Efficiency of services within a reasonable budget otherwise statehood would completely sink the island.
Clarification: I am against statehood, but if it comes, it needs to be after PR learns to run a goverment that is as efficient as most states or it will never work financially.