If you look in any economics textbook for a definition of money, you'll find something like this:

store of value, which means people can save it and use it later—smoothing their purchases over time;

unit of account, that is, provide a common base for prices; or

medium of exchange, something that people can use to buy and sell from one another.

http://www.imf.org/external/pubs/ft/fandd/2012/09/basics.htm

You might also find a list of properties like this from a St. Louis Federal Reserve publication comparing a $20 bill to a cow as money:

Durability. A cow is fairly durable, but a long trip to market runs the risk of sickness or death for the cow and can severely reduce its value. Twenty-dollar bills are fairly durable and can be easily replaced if they become worn. Even better, a long trip to market does not threaten the health or value of the bill.

Portability. While the cow is difficult to transport to the store, the currency can be easily put in my pocket.

Divisibility. A 20-dollar bill can be exchanged for other denominations, say a 10, a 5, four 1s, and 4 quarters. A cow, on the other hand, is not very divisible.

Uniformity. Cows come in many sizes and shapes and each has a different value; cows are not a very uniform form of money. Twenty-dollar bills are all the same size and shape and value; they are very uniform.

Limited supply. In order to maintain its value, money must have a limited supply. While the supply of cows is fairly limited, if they were used as money, you can bet ranchers would do their best to increase the supply of cows, which would decrease their value. The supply, and therefore the value, of 20-dollar bills—and money in general—are regulated by the Federal Reserve so that the money retains its value over time.

Acceptability. Even though cows have intrinsic value, some people may not accept cattle as money. In contrast, people are more than willing to accept 20-dollar bills. In fact, the U.S. government protects your right to use U.S. currency to pay your bills.

https://www.stlouisfed.org/education/economic-lowdown-podcast-series/episode-9-functions-of-money

Cryptocurrency's Monetary Properties

So how does cryptocurrency stack up on the money scale?

First, let's look at the properties to see if it can even become money.

Durability - Since blockchains are electronic records kept redundantly on every node of the system, we're pretty good here. As long as we can run and operate computers, we should be OK on durability. If we can't, civilization has collapsed and you won't be able to spend your crypto anyways.

Portability - This might seem like a slam dunk for crypto, but I would argue that it is not yet portable enough. We need dead simple mobile apps that your grandmother can use to spend crypto with no technical expertise or remembering keys or 21 word pass phrases before I will call this done. It has to be as easy as swiping a card or handing someone a bill of fiat.

Divisibility - Crypto is best in class when it comes to divisibility, far beyond fiat. Being able to go way past the decimal point makes rounding that we see in fiat generally unnecessary.

Uniformity - Again, crypto scores really well. You can make an argument that the different blockchains are not uniform between themselves, but within one particular blockchain any coin is as good as another. In fact, coin spinners rely on this property hide trails of ownership.

Limited Supply - Crypto is easily the best out there at limited supply. Most blockchains have a hard limit built into them like bitcoin's 21 million cap that will be approached asymptotically. Funnily enough steem does not have a hard cap and instead will eventually reach an inflation rate of 0.95% annually. 

Acceptability - Now here's a problem. While great strides have been made to broaden the acceptability of crypto in the world it is still a tiny niche market of vendors that accepts it. It will still be several years before acceptability is universal enough to reach a reasonable level compared to fiat money.

So on basic properties, crypto scores a 4 out of 6 with the remaining 2 categories needing improvement. If those 2 categories were a hard "no" then crypto could not even hope to be money. Since they are possible and improving, cryptocurrency has the ability to become money.

Cryptocurrency's Monetary Functions

Next let's look at how crypto works at satisfying the 3 functions of money. I'll take them a bit of order compared to the list above.

Unit of Account - Crypto is great as a unit of account. You want 12 bitcoin? Sure. 486 Satoshis? No problem. 26.2854 ETH? Easy. Being a digital asset subject to digital precision is great for the unit of account function.

Medium of Exchange - This goes back to the acceptability property. Crypto is a medium of exchange. I can pay you in cryptocurrency for a good or service. But we're still in the early days of acceptability, so the scope of exchange is pretty small. So crypto's functionality here is a "technically yes, real world sort of" kind of answer.

Store of Value - This is the biggie. People will argue with me on this one and point to charts and exchanges showing the cryptos have value. Yes, they have value, but are they a store of value? Can I put my crypto on my ledger wallet and come back in a year or ten and have a reasonable expectation as to how much value I will have at that point? Absolutely not. The vast majority of cryptocurrency is being used as a speculative vehicle priced in fiat terms. It's ironic that it was dogecoin that first focused on 1 dogecoin = 1 dogecoin. 

Crypto Money vs Fiat Money

So let's look at how crypto compares to fiat as money:

So we can see that crypto is edging out fiat when it comes to the properties of money, but is losing on the monetary functions. So what does this mean? It means that crypto has the potential to be a better money the fiat because Satoshi took a lot of this into account when he originally designed bitcoin, but there is still plenty of work to do before cryptocurrency will replace the dollar, euro, yen, or yuan.

Is cryptocurrency money?

Not yet, but soon.