Having once been a social worker and having put children in care. I well know that a home, and institution provides residential care for children. The term foster is for placing children in a family with parents which take the place of the real parents foster. This one step away from adoption.
First step: into a home for children (old fashioned orphanage), termed residential care.
Second step: place with a family of "foster parents".
Third step: the "foster parents" adopt the child.

Obviously real cases are not always as simple as this.

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Note added at 4 days (2015-02-06 18:01:58 GMT)
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The center is a certified residential care centre for minors".
Basically, only familes can foster.

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Note added at 4 days (2015-02-06 18:09:34 GMT)
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Final note "affidamento familiare" is foster care, but this is affidamento in "un centro dove i bambini vivono fino a quando trovano una famiglia adatta o" The center provides residential care until they can be placed in a family with foster parents.
In the UK and elsewhere children in urgent need of care can be placed directly in ordinary families with foster parents, but this is not the case here, the go to a "centro" not a family.

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Note added at 4 days (2015-02-06 18:14:36 GMT)
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Corrections:

I well know that a home, an institution, provides residential care for children.

The term foster is for placing children in a family with parents who take the place of the real parents, they are foster parents (as in foster milk).

This is one step away from adoption.

"but this is not the case here, they go to a "centro" not a family.