Is Bitcoin a currency? This question seems to be asked every now and then when legal status of Bitcoin is discussed - Is Bitcoin a currency? What are the characteristics that would make it a currency, and what makes it different from the standard definition?
TL;DR Bitcoin already is a currency because it's a generally accepted medium of exchange among certain communities. As those communities grow and usage spreads to other communities, its strength as a currency solidifies. 

This requires a little bit of history. I am not a numismatist, but I have studied this a little even before the advent of Bitcoin.

Currency is a set of things that are a generally accepted medium of exchange. 

Throughout history, an accepted medium of exchange has been anything of value to both people involved in the transaction. Typically, these are physical goods that have some semblance of inherent usefulness and a degree of rarity. Also, there is typically a perceived finite supply of the thing. Lastly, the importance of portability is generally high: if it is cumbersome to carry enough of the thing to make daily purchases, it is less likely to be an acceptable medium of exchange because no one will want to carry it around with them!

So, I've set the stage for most world currencies: small, portable coins comprised of precious metals. The metals can be used in products and are rare in that it takes work to extract them from the earth. The supply is thus finite, until another deposit of the metal is discovered. That's when the overall value of the coin may drop compared to other things, but at its simplest explanation means that
the coin metal has become less rare.

This kind of coinage started organically. People could give each other a weight of metal and know what its value was to them. Eventually, as governments were established, governments would gather up all the metals they wanted by whatever means necessary, and then melt the metals in order to mint coins with an intended, consistent value because of their weight.

As the price of goods increased steadily, it was impractical for a person to carry a sack of coins, so someone contrived the bright idea of paper money, and later, a bank note.  These are simply a promise that a person can exchange that note for the coins related to it. Thus, this paper money or bank note used to be simply a proxy to more valuable coins or other forms of metal.

However, this is prone to interference by those who print the notes and the governments that oversee it all. Eventually, paper notes became backed by promises for coins and metals that didn't exist. So, the value of the notes in relation to the coins and metals decreased. Then banks stopped accepting notes in exchange for coins.

What resulted is called fiat currency, which has a value simply because some government declares it to have value. It actually more closely related to debt, but that's a complex subject for another question.

A chief problem of fiat currency is that a bank or a government can simply print more bank notes in order to create more money. This works in the short term, but any savvy person will realize the similarity of this to someone finding a new deposit of a metal. When there is suddenly more of something, what existed of that something is suddenly less valuable because it is less rare. This does not matter a whole lot when there is only one thing of value. When there are many things of value, e.g. silver, gold, platinum, diamonds, oil, other fiat currencies, the value of our something compared to those will be affected.

All of these things are usable as currency but some are more practical than others.

Bitcoin is similar, but more abstract. Bitcoin has no inherent usefulness: it's just data. It does have rarity: the supply is finite because only 21M coins can exist. The available supply is growing by the minute, but there will be a day when no more will be "found" there by halting its inflation in value. Instead, at that time, its value will begin to deflate as coins are permanently lost for one reason or another.

Bitcoin's inherent uselessness as a physical good -- data -- contributes to another factor: its portability. It's just data and we can sure store a lot of data in a small physical space. This property makes it almost infinitely portable. A billionaire could carry their life savings in their pocket on a Flash drive and no one else could have control of the physical thing that is their life savings.

Creating a currency when the physical thing has no inherent usefulness requires that initial participants assign a value to it. It's a fiat currency, but the value isn't controlled by any central authority. No central authority can create more of it. No central authority can destroy it. This is not to say that an authority cannot destroy it, because a government sure could pass laws to prohibit its exchange/possession/production.

In its infancy, Bitcoin has limited intra-economy value, that is, it has limited value as something that can be exchanged for payment for work or goods simply because not a lot of people have boldly decided to accept it with the hopes that they can spend it on something they need. This value grows daily as more businesses start and more people believe that they can spend what they accept in it.

Bitcoin at this stage is no different from arcade tokens, in-game currency, or Monopoly money used in schools to teach children how money works: it has a limited value to a limited audience. It is currency to those who participate in this limited audience, and its inherent value (not necessarily its value relative to other traditional currencies) grows as the audience grows.

To add another question to the original: How can the strength of Bitcoin as a currency grow? The answer is quite simple: use it! Find something to buy with it, find something to sell and accept it as payment. Keep this cycle going and get others involved.