A decentralized currency is one that is not emitted by a central authority, like a bank, government or any other central institution (hence the term decentralized). Decentralized currencies can be minted, printed or otherwise generated by any user, according to certain rules.
In the case of cryptocurrencies, there is a protocol that governs the rules of coin emissions. A computer code establishes all the important aspects of the currencies. Practically, what the code does is it creates context of a new type of market, with its own laws. What is the rate at which the currencies are put into circulation? Is there a limit on how many coins are emitted in total? How are they secured? What sort of proof can the person that generated the coins provide that he legitimately minted them? Who exactly gets the right to generate the coin? The rules implemented in the protocol ensure the success or failure of that market.
In the case of decentralized cryptocurrences, any user can reasonably get involved into the creation of the coins. Assuming that the great majority of people have access to a computer and to Internet, they can create coins using their own equipment. That equipment can be a device of their own choosing, techincally they should not be restricted to choose one from a certain company. Of course, the market self-regulates and it can offer devices that are more capable than others to mine in an efficient manner. This way, anyone can become a member of the community, with equal rights and opportunities.
The idea of a decentralized cryptocurrency opposes the traditional monetary system, where someone at the top controls the coin emission. When there is a central system generating a coin, someone can, in bad faith, create inflation and devaluate the (crypto)currency, misappropriate sums of money or otherwise manipulate the market. Decentralized currencies offer an alternative, where nobody has this kind of control over people’s finances. This brings the market closer to being self-regulated, according to the purest economical law – offer and demand.
Bitcoin was the first cryptocurrency to offer an alternative for the legacy system.
What about centralized cryptocurrencies?
You might have encountered centralized cryptocurrencies that cannot be mined by users. In turn, they are mined and distributed by a central authority (a company or a central bank), on their own accord. Normally, they are treated with great suspicion (for good reason). You need to look into the reasons why a cryptocurrency is mined centrally.
Some governments are considering creating their own cryptocurrencies. The most recent news in that regard comes from China. They are simply looking into replacing the legacy method of payments and printing money with a new technology, without altering the existing system. They are considering this solution in order to cut the costs of minting and administrating the money.
Therefore, they will of course look into creating a centralized cryptocurrency under their own control. There is great doubt a centralized currency can be based on the blockchain technology.
Some companies may decide to create their own cryptocurrencies, used internally inside the company or as a voucher system to reward their clients. It is debatable whether they are indeed cryptocurrencies in the true sense of the words or not. Technically speaking, they do not intend to create a market. At best, they are rather redeemable tokens, or, as we said before, vouchers.
Veterans in the community advise that you do not invest in centralized cryptocurrencies. Most (almost all) centralized cryptocurrencies raise red flags and might be scams.