I wasn't around at the time, so this is pretty much what I picked up from pop culture.

The economy was doing pretty well. When the outgoing PM failed to properly support his successor at the 1994 elections, the Christian Democratic party lost big, leading to the first government coalition without them since political reforms in 1918. The resulting Labour+Liberal coalition took the country on a neoliberal spin: denationalizing the postal and telecom services as well as the railroads and the big chemical plant. They also legalized gay marriage (but only in 2001). The "third way" (as opposed to CD coalitions) was popular, and influenced the policies of Tony Blair and Bill Clinton.

The 90s are what foreigners usually think of when they think of Amsterdam (which, let's be fair, is what people think of when they picture the Netherlands). Kind of grimy, kind of seedy, buying drugs at the red light district, Eurobeat in the background. In reality, locals got pretty sick of the way things were going and started looking for politicians who prioritized (drug) crime, law and order, and badly integrated immigrants. This eventually came to a head in the early 2000s, which saw the first national populists as well as the return of the Christian Democrats.

On a European level, the Treaties of Maastricht (1992) and Amsterdam (1997) were signed. Oh, and we prepared to switch our currency from the gulden to the euro.

Other things include the crashing of an airplane in the Amsterdam Bijlmer neighborhood in 1992, and for a lot of families, the introduction of home computers around the time of Windows 95 or 98.