In the context of cryptocurrencies, a deflationary spiral may happen when there is a self-reinforcing process of draining the supply of coins or tokens from the markets while the coin price keeps going higher.
Although this has not yet happened in practice, it is a theoretical possibility often cited as one of Bitcoin's potential long term weaknesses.
In the legacy markets, a deflationary spiral usually happens during periods of financial crisis. Less money flows in the markets which, in turn, causes lower sales and merchants are then forced to lower their prices due to low demand.
Lower prices lead to lower growth, lower wages, lower profits which in turn leads to even less consumption. This is a self reinforcing process and requires central authority intervention in order to be stopped.
The usual method of intervention usually comes in the form of printed money. Central Banks print money using some process with a fancy name, such as Quantitative Easing, the printed money usually does not reach The People, but magically ends up in the banking system which artificially pumps the stock market and the financial sector in order to present an appearance of growth and normality.
This was the central banking strategy for the 2008 market crash recovery : printing money.
When Central Banks print money, this generates inflation, which works to combat the deflationary process. In practice this process does work but it tends to concentrate enormous amounts of wealth in the financial sector, with very poor distribution. As a result, in the past few decades we've seen the greatest concentration of wealth in the history of mankind. Quantitative Easing (QE) basically meant free money for banks. Who pays for the inflation generated by QE? The newer generations do. Millenials will work several times as much as their parents in order to buy a home, a new car or to travel.
Cryptocurrencies, on the other hand, do not allow this sort of market manipulation. Cryptocurrency monetary policy is hard coded into computer software and only so much can be minted with every block. If central banking institutions are one day established to govern cryptocurrencies, they will have to actually obtain funds by market rules, not by printing money as they please.
Note that saying that currency gained value is the same thing as saying that products are cheaper. You can buy a lot more with one Bitcoin today than you could in 2014. This can be seen either way: Bitcoin gained lots of value against the dollar, or that products priced in dollars are now cheaper against Bitcoin. The term "deflation" refers to the price of products and services against a given currency.
How can a deflationary spiral happen with Bitcoin? The process would go something like this:
Bitcoin will halve block rewards approximately every 4 years. At the time of this writing 12.5 BTC are pumped into the market approximately every 10 minutes. This is the only monetary inflation possible in the Bitcoin system. No central bank or any other "authority" for that matter can changed this without going through the BIP process and convincing the community to print more money.
Combating the deflationary spiral with cryptocurrency might be a challenge in the future. The important issue is to work for wide adoption of Bitcoin in commerce and services, forcing the currency to circulate and not only be hoarded as an equity. Satoshi's are 8 decimal divisions of a Bitcoin and allow for wide circulation of currency. Bitcoin totals roughly 15 decimal places which, if each Satoshi one day equates one US Dollar of today, would equate 1,000 trillion U$ dollars in circulation, minus lost coins. This is more than enough for a worldwide economy. But first layer Bitcoin is not necessarily going to be the currency itself, but solutions may be built on top of this first layer in order to accommodate even more currency if it ever is needed. Tether, for example, is built upon the OMNI layer which itself relies on the Bitcoin blockchain.
While a deflationary spiral can be a concern, by the time it happens we expect many more second layer solutions to exist on top of Bitcoin Core. While Lightning Network speeds up Bitcoin transactions on the 2nd layer, other solutions will arise to compensate for eventual monetary issues such as deflation. Although our opinion is subjective, we do not believe Bitcoin is at risk of a deflationary spiral for the foreseeable future. Of course Bitcoin tends to gain a lot of market value against other currencies in the near term, but eventually this movement will reach a point of balance where it'll be possible to make better assessments about whether market deflation will be a problem or not. For the time being, Bitcoin is still too volatile to make any kind of assessment.