Just so you don't get confused: I'm typing this as if this guy actually exists, but like Santa Claus, he's not real, 'kay? Here we go!
What is it?
Sinterklaas is a holiday similar to Christmas, celebrated mainly in the Netherlands, and also in Belgium, the Netherlands Antilles and Aruba. It starts around mid-november, and ends on the evening of December 5th, the birthday of Sinterklaas. On all days except this last evening, children place their shoes by the chimney or fireplace or, since not many people still have those, next to or under the central heater. In their shoes, they place a list of gifts they would like, a letter or drawing to Sinterklaas and treats for the Sint's horse, Amerigo (such as a carrot, straw, some water, lumbs of sugar). In the night, Sinterklaas walks over all the rooftops with his helpers, who slip through the chimney to replace the treats/letters/drawings with small gifts and traditional candy. As you can see it's pretty much the same as Christmas, where if I'm correct, you leave cookies for Santa Claus, right?

Once the shoes are set, the family sit by the chimney/fireplace and sing traditional songs. The children are told that Sinterklaas can hear them through the chimney because he walks on the rooftops.
Sometimes, schools also participate in this. Children can leave a shoe at school and come collect their candy the next day (schools usually only give candy because if you have to buy that many presents, you'd lose a lot of money).
The last evening, Sinterklaas and his helpers (see below) don't walk over the rooftops, but knock on everyone's doors and windows and run, leaving a bag made of jute or a basket filled with big(ger) presents and candy. The family spends the next hours unwrapping all the presents, after which hopefully the children'll be sedated for another year! The next morning, Sinterklaas leaves for Spain again, and everyone'll have to wait until the next year for him to come back.
Who is Sinterklaas?
Sinterklaas, formal name Sint Nicolaas, is the Dutch name of Saint Nicholas, who you English folk like to call Santa Claus. They're not the same person in terms of these holidays, though. We call Santa Claus 'de Kerstman', which literally means 'the Christmas-man'. In fact, your Santa Claus actually comes from the Dutch word Sinterklaas! Ahem. Though he is really from Anatolia, in popular belief - and thus in the children's minds - he is from Spain.
Some of his names are Sinterklaas, Goedheiligman, Sint Nicolaas or just plain Sint.
His appearance is much like that of a bisshop. I could name all the pieces of clothing, but they mostly have Dutch titles that I can't find a proper translation of, so have a picture instead:

Close up of the gloves:

Arrival
Every year in mid-November, he arrives from Spain in the Netherlands by steamboat, heavily decorated with little flags, red banners, etcetera. Of course, there are hundreds of Sints all around the country and none of them is 'the real one', but ah well. In Dutch, we call this boat the Stoomboot (steamboat) or the Pakjesboot (lit. (little-)packages-boat or (little-)presents-boat). Families gather with their children to watch, and maybe receive some candy or shake the Sint's hand. They can also give drawings and lists of gifts they may want to receive (we call this a verlanglijstje) to Sint.

Helpers
The Sint has an abundance of helpers who we call Zwarte Piet (plural zwarte pieten). Literally, this means black Piet (Piet is a traditional Dutch name, like Jan and Hans). Though they are usually made to appear like black people, the real reason they are black is because they come down the chimney to deliver presents (much like Santa Claus) and are thus covered in soot. They carry Sinterklaas's stuff around, because he is quite an old fellow, and help him go up and down the rooftops, wrap presents, etcetera.
Sinterklaas also has a Gray Horse whose name is Amerigo. He rides this horse over the rooftops when he's delivering presents to the children, and sometimes also during the arrival or through the cities.

There are many Sinterklaas-songs, which are sung pretty much everywhere. During the arrival, in schools, and in the evening by the chimney (see above). The songs are about the man himself, about his helpers, presents, candy, and so on. There are too many to just translate here, but you can view some on YouTube:
Hij komt, hij komt (He comes, he comes)
Sinterklaas kapoentje (Sinterklaas ladybug) I know the title doesn't make sense, but it's just for rhyming purposes.
Zie ginds komt de stoomboot (See over there comes the steamboat)
Sinterklaasje bonne bonne bonne (Again, bonne is just for rhyming purposes)
Candy
Sinterklaas has a lot of traditional candy. Not much explanation needed, I should think. Here are some examples:
Kruidnoten: small, hard ginger-bread like cookies

Pepernoten: soft, doughy things that taste a little like... hard to describe. I'd say ontbijtkoek, but that's Dutch too. I guess you have to taste it to know it XD

Speculaas: originally only for Sinterklaas, but these years you can buy it anytime you want. Speculaas is a sort of cookie, much like the above-mentioned kruidnoten, except thinner (though big, hard plaques exist as well). It's made out of pepper, cinnamon, ginger, cloves, cardamom and nutmeg.

Schuimpjes: It's like pressed sugar. Oh, it appears the English translation should be meringue. It's a little less puffy than meringue, though. They're full of sugar and aroma compounds. Make the children bounce all day.

Taai-taai: Tastes a little like pepernoten but much tougher, like it's been lying around unprotected in the sun XD That sounds not-so-nice, but the taste is good :)

Aside from that, there are also many chocolate products: letters, figures, coins... and tablets and marzipan.
Surprises (pronounce: surr-pree-ses).
This is more for the teenagers and adults than for children, so I put it all the way at the bottom. Although... around 3rd/4th grade children get told about the fact that Sinterklaas isn't a real man yadda yadda. From then on, people start making surprises.
Basically you make something out of boxes, paper, carton, etcetera. In there you put a present, and you usually make it tricky or disgusting for the person you give the surprise to to get to the present. Straw or ripped up newspapers are popular, as well as hairgel, porridge, and whatnot.
In november (or earlier, it just depends) people draw 'lootjes', little fold-up papers with another person's name on it. For this person, you make a surprise and a poem to go with it. You usually match these two with an interest or trait of that person. For instance, you could make a cardbox-PlayStation for me. If you're crafty XD (My Mom actually did that for me two years ago! She made me a cardboard PSP which looked like a GameBoy Color, aww).
In my opinion, this is the fun part of Sinterklaas, especially if you do it with your friends. And it's funny watching them bury their hands in gel, straw and syrup XD Not so funny if you have to do it yourself, but ah well.
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