The Dutch Republic (up to 1784)

Ok so you're familiar with the Eighty Year's War and the fact that the Netherlands were a republic during that time. In fact, the Netherlands were called "De Republiek der Zeven Verenigde Provinciën" - the "Republic of the Seven United Provinces", or simply "de Republiek - the "Dutch Republic". The Dutch Republic was governed by regenten (patricians) who had representatives in the States ('parlement') of every province. Every province also knew the office of stadtholder.

A stadtholder was a person appointed take care of certain executive things, such as maintaining peace and order. Every province appointed their own stadtholder. (A stadtholder originally was someone who temporarily took care of things in absence of the ruler; 'stadt' being related to the word 'instead'. The Dutch took this office and made it a permanent appointment by the States instead of a temporary one by the - no longer existing - ruler). Usually all but one or two provinces would choose the same stadtholder: the Prince of Orange.

This was the case throughout the 17th and 18th century (with a couple of exceptions). At the end of the 18th century problems were brewing though. So-called Patriots were dissatisfied with the corruption of the regenten and the influence the Prince of Orange had in politics. They wanted a true Republic, with power shared by all the people. This led to a conflict between the Patriots and the Orangists (supporters of the stadtholder).

Patriotic Revolution and French dominance (1784-1813)

At first the Patriots gained ground, and in 1784 they controlled much of Utrecht, Holland, Zeeland, as well as cities in North-Brabant, Groningen and Gelderland. The Prince of Orange fled from The Hague in Holland to Nijmegen in Gelderland. The English and Germans weren't happy with the revolutionary ideas in the Netherlands and wanted the Dutch Republic to remain as it was. In 1787 a Prussian (German) army came to the help of the Prince of Orange. The Prince returned to The Hague and many Patriots were driven from the country - they left for France.

Then in 1789 the French Revolution happened. The Patriots in France secured the assistance of the new French Republic. In 1795 a French army invaded the Republic and put the Patriots in power. The Patriots created a new republic, the Bataafse Republiek (Batavian Republic). This republic existed with French support until 1806 - it was effectively a French puppet state.

Napoleon Bonaparte wasn't happy with how things were going in the Batavian Republic, so in 1806 he made his brother Louis Bonaparte (called Lodewijk Napoleon in Dutch) king of the Netherlands. The new state was called the Kingdom of Holland. Louis Bonaparte was a pretty decent king, serving Dutch interests instead of French interests. This of course made emperor Napoleon unhappy again, and in 1810 he ended the Kingdom of Holland and instead incorporated the Netherlands in the French Empire.

The United Kingdom of the Netherlands (1815-1839)

In 1813 the French were driven from the Netherlands by an anti-French coalition (mostly Prussian and Russian forces). William Frederik, Prince of Orange, was welcomed back to the liberated Netherlands (he lived in exile in England during the French period). He was asked to govern the Netherlands while the war against the French continued.

At the Congress of Vienna, where the victorious allies decided what to do now that Napoleon was defeated, the allied powers asked William Frederik to become king of the Netherlands and the Southern Netherlands (Belgium). This United Kingdom of the Netherlands was to form a strong buffer against future French expansion. The allied powers wanted this new state to have a strong ruler so that it would not become a disfunctional republic as the Netherlands were before.

So this is how in 1815 the Netherlands became a constitutional monarchy under king William I.

Things didn't go exactly as planned; there was a huge difference between the northern provinces and the southern provinces, they couldn't get along and had developped different cultures and attitudes in the two and a half centuries they were governed separately. In 1830 the souther provinces seceded and became the Kingdom of Belgium. Since the United Kingdom of the Netherlands were no longer united, the northern provinces became the Kingdom of the Netherlands. This is the state which still exists today.

Conclusion

The Netherlands became a monarchy because the Dutch Republic got caught up in the revolutions at the end of the 18th century. After those revolutions, a strong leader was needed, so it was decided the Prince of Orange would be made a King.

thanks for thegreat awnsers.

There was a similar question two or so days ago which may contain some answers that may satisfy your question: http://www.reddit.com/r/AskHistorians/comments/3ks4pg/how_did_the_dutch_royal_house_come_to_power/