Many democracies run, with varying degrees of formality, on a coalition system. Many parties via for seats in a legislative chamber, representing many distinct interests. Generally, there is something that can only be done with a strict majority, often things like passing bills or electing a Prime Minister. Since the interest groups are so fragmented, for a given bill, many of the groups may have weak or even no opinions about it; for instance, a labor party may have no strong opinions either way about a gun control bill. (I'm not saying that everybody who calls themselves "labor" parties, and I think there are a lot of them, won't have an opinion, just that they may not.)
These bodies usually run on a vote trading system. The labor party will vote for your gun control bill if you vote for our minimum wage raise. As in all human interactions things can got complicated, and this is simplified, but this is the general effect. These voting arrangements form coalitions, and barring a really strong showing by one party, it is these coalitions that really run the relevant body, not a particular party, with strength generally proportional to the number of seats controlled. If I've got my specifics straight, I believe that a coalition that elects a Prime Minister is even referred to as a "government" in Israel and the UK, leading to people talking about "toppling governments" when a coalition falls apart, which sounds quite strange to American ears.
Because the Labor party and the Republican party share the same word, it is commonly thought that they are basically the same thing, and therefore the US is only a two party system. This is only the first of many times in this post series where I will point out that the terminology is misleading. They are not "parties" in this sense.
If you think about it, the problems with the US being a two party system, with the coalition-based definition of "party", is obvious. A party usually has a reasonably well-focused platform. There are many parties because there are many, many types of platforms someone may be concerned about. Having only two parties would tend to imply only two basic types of interests, which is clearly absurd. Every party in any government you can point at will also be represented to some degree in the US. Clearly, no group of three hundred million beings in the modern world is going to be sliced in two that neatly; the US can't be a two party system.
And it is not. Republicans and Democrats are actually meta-coalitions. A coalition bands together in the relevant body to push their policies. A meta-coalition actually bands together at a level one higher (hence the "meta"): In the US, the dominant problem is getting the votes of the people in the first place, so what would be "parties" in the British or Israeli system actually band together at election time to get elected. The purpose of the Republican and Democratic parties is to assemble a coalition of special interests that will be considered superior to the other by a majority of the voters.
Referring back to the title of the myth, the US is not a coalition system in the normal sense. But it isn't a two-party system in the typical sense either.
(This is #1 in the government myth series.)