For those who are not familiar with the Iberian naming convention: it's to have two surnames or family names - one from the mother's family and one from the father's family. In Spain, the order is Father's + Mother's, in Portugal, it's the reverse order. After marriage, the tradition was to not change your family name (although in Portugal, people started to do so by the late XIX century). If you read a name like

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Jose Hidalgo Martinez

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You know that his father's surname is Hidalgo, and that his mother's family name is Martinez.

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Now, one thing about surnames - in general, in medieval Europe, and specifically in the Iberian kingdoms, the family names were in a much more "fluid" situation that nowadays - there was no law mandating them, and people could change the family name a lot easier than we are used to. Having said so, it's well attested (at least in XV century Spain, although I guess that in Portugal the situation would be very familiar) that any person could call upon either the father's family or the mother's family as a matter of pride or as a way to boast about the proud origins. That is different from other countries in Europe, were people appear to have though of family as a patrilineal thing, always relating themselves to their's fathers families. What is the reason for this difference in Iberian conception of family? As far as I know, it's not clear, and, in fact, it's not very well studied.

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It was, thus, only natural that with this conception of what is a family, women never lost their family name when married and that the noblemen in Castille started, around XVI century, to use two family names - to highlight their proud origin in both branches. From there on, this convention appears to catch in the rest of Iberian kingdoms and population, forming the Spanish and Portuguese naming conventions.

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You can look for works of George R. Ryskamp to have a good view in English about the origin of the Iberian naming conventions. Unfortunately, most of it is not freely accessible.