This all goes back to the 16th century. But first we've got to get a few things straight - because your question has a few things not exactly right.

Nowadays there's the country of Belgium and the country of the Netherlands. There is no country called "Holland". Holland is an area in the country of the Netherlands - arguably historically the most important area, which is why "Holland" is often used to refer to all of the Netherlands. Holland makes up 2 provinces (North Holland and South Holland) of the Netherlands' 12 provinces. As I said, it is common for "Holland" to be used for all of the Netherlands, but it is not actually correct and doing that gets confusing when you're talking about the history of the Netherlands, as I'm about to do.

With that out of the way, let's go back to the 16th century. At this time the area which is now roughly the Netherlands and Belgium (and a bit of northern France) consisted of about 17 counties or provinces. These provinces were collectively referred to as the "Low Countries" or the "Netherlands" (literally "low-lying country"). I'll use 'Low Countries' here to avoid confusion with the modern country of the Netherlands.

These provinces were united under Charles V, the Holy Roman Emperor and king of Spain. A bit later Charles V was succeeded by Philip II as king of Spain and lord of the 17 provinces. Philip II was unpopular in parts of the Low Countries because he centralised the government, imposed taxes to pay for Spanish wars, and persecuted protestants. Long story short, some provinces revolted against Philip II, while others stayed loyal to him. This happened from about 1566. After a couple of decades of revolts and warfare, the northern provinces of the Low Countries formally declared independence. These provinces became known as the "Republic of the Seven United Netherlands", usually shortened to "United Provinces" or "Dutch Republic". The other provinces of the Low Countries, still under Spanish control, are usually referred to as "Southern Netherlands".

The Southern Netherlands became the Austrian Netherlands in the 18th century. During the Napoleonic Wars the entire area was under French control, and afterwards it was decided that the Southern Netherlands and the United Provinces should be merged so that they'd be a more powerful force against the French. This was the "United Kingdom of the Netherlands". The people in the Southern Netherlands didn't agree with this arrangement though (nobody had asked them) and after just 15 years they seceded from the United Kingdom of the Netherlands. From then on, the Southern Netherlands were the Kingdom of Belgium. Meanwhile the United Kingdom of the Netherlands was no longer united, so it became just the Kingdom of the Netherlands.

So there you have it. The "Netherlands" back in the day were a region of many provinces. The southern part became the country of Belgium, while the northern part of those provinces became the country of the Netherlands. One of those provinces in the Netherlands was Holland (now split into two provinces). During the time of the Dutch Republic Holland was the most important of the 7 provinces. Holland paid for more than 60% of the expenses of the Republic; Holland had the largest cities and the largest fleet; when foreigners interacted with Dutch merchants, they most often dealt with merchants from Holland. This is how "Holland" came to stand for all the Netherlands.

One thing I haven't addressed yet is why the word "Dutch" is used to refer to people or things from the Netherlands. This also goes back to the 16th century. Back then the word "duytsch" or "dietsch" (some word with various spelling variants) was used by the Dutch to refer to themselves and their language. "Duytsch" meant 'people' or 'belonging to the people'. The "Duytsch" language was the language of the people (as opposed to the language of the church [Latin], or the elite [French]). The English language took the word "Duytsch", changing it to "Dutch" in the process, and also started using it to refer to people or things from the Netherlands.

I hope this answers your question :)

The Netherlands is not two countries, the Netherlands itself is a country and Belgium is also a independent country.

What the two countries have in common is that they speak Dutch in the Netherlands and in the northern part of Belgium.

And Holland is in fact not a country, Holland are two provinces in the Netherlands (north-holland and south-holland) they are the most known provinces in the Netherlands. That's where the misconception comes from, that people call Holland the Netherlands.