would

We use 'would' in that way about something which started in the past and which we know continued for a time.

On Jun 1st Joe got a cold which would last three days.

First things first--the word you wanted is Portuguese. Since the sentence is lifted directly from a Wikipedia article, i am surprised that you spelled that incorrectly.

In this case, would expresses futurity in the past. Goa was colonized in the 16th century, so that is definitely in the past. Goa ceased to be a Portuguese colony in 1961, which is also in the past. However, it's four and one half centuries as a Portuguese colony was a part of the city's future at the time the Portuguese took over. This is common usage of a modal auxiliary verb. Governor Reagan of California would go on to win the 1980 presidential election and become the 40th President of the United States.