William of Orange (aka William the Silent, William of Orange-Nassau - not to be confused with the William of Orange III, who ruled over England) joined the Dutch revolt against the Spanish, which resulted in the formal independence of the Netherlands.

The House of Orange used the colour orange in its coat of arms, and the flag of the Dutch Republic drew inspiration from the colours on William of Orange's own coat of arms. (The current flag of the Netherlands is similar to that of the Dutch Republic, but the orange has been switched to red)

(Links to Wikipedia used only for picture-purposes - I found an article in Dutch regarding its history here. Google Translate does screw up the grammar, but it's still quite readable.)

Long story short, the colour orange is a national colour for the Netherlands because of the prominent place that the House of Orange-Nassau played in the history of the Netherlands. William I of Orange, or William the Silent, played a crucial role in leading the country to independence in their conflict with Spain. The Dutch national anthem, Het Wilhelmus, is a song about William. The Princes of Orange were the Stadtholders of the United Provinces, the Republican period aside, for most of the 17th century, and has been the royal family of the Netherlands ever since the formation of the monarchy in 1815. Naturally, the colour orange has been long associated with the royal family, and as such has become a national colour, even though it's obviously not on the Dutch flag.

hi! you might find this post interesting

Orange seems to be the national color of the Netherlands, so why isn't it on their flag?