Deflation is the 'wolf at Europe's door'
The first reason is the dangerous way that deflation interacts with debt levels. If you have a debt then you need to directly repay what you owe: €100 of debt requires €100 to pay back. That's obvious but consider what happens when prices are changing either up (inflation) or down (deflation). When you have inflation, when the price of what you want to buy is rising, the €100 in your pocket buys less. In debt terms, that means the real value of the €100 debt decreases when you have inflation. Which is great because it means it's easier to repay your debt.
But everything is flipped if you have deflation: the real value of your debt slowly increases over time. Which is definitely not great. Debtors end up cutting back on spending elsewhere just to pay their growing debt. That means they're not investing and more likely to default or go bankrupt. It also means that people who might be thinking about borrowing - maybe to buy a house or a company wanting to invest in new machinery - will be less inclined to do so because they know their debt is going to grow. All of this hurts the economy.
This process is known as 'debt deflation' but, slightly confusingly, Europe doesn't even need to be experiencing deflation for it to suffer its negative effects. The ECB sets a target for inflation of just below two per cent. That means that companies and individuals have a reasonable expectation that inflation will be two per cent. They therefore enter into agreements to borrow money based on this expectation. But if that two per cent target is consistently missed then the amount of the debt that is owed is bigger than anyone had planned for. That gives borrowers the same problem that they would have if there was deflation: the debt is bigger than they had planned for because they don't have that two per cent cushion. That's why people are so worried about 'lowflation': when inflation is lower than what the central bank tries to achieve.
The second major reason to worry about deflation is that it tends to lead to more unemployment. If the price that a company can sell something for keeps falling because of deflation then they are going to have to try to reduce their costs. The natural response would often be to cut wages to try to make sure the company can maintain a profit margin. But company bosses often don't, presumably for understandable behavioural reasons (cutting people's wages often hits morale hard). So bosses tend to reduce the number of people they employ by laying people off and not employing any more, thus increasing unemployment.
Given all of this, it's not surprising that central banks try to avoid deflation. But there's a limit to their powers and it's this that is probably the most pernicious threat from deflation. Central banks adjust the interest rate that they set as a way of bringing inflation into line with where they want it to be. But they can only cut it so far (we used to think that was to zero but, turns out, they can go below zero).
If the central bank is not able to cut rates as quickly as inflation is falling then it can mean that the rate of interest once you account for inflation increases. That is actually a tightening in monetary conditions. That means you can reach a point where inflation just keeps on falling because the central bank has cut its interest rate as much as it can. It's at this point that the economy can slide into a self-fulfilling spiral where the price of goods fall, so the inflation-adjusted interest rate increases, causing the economy to weaken, which leads prices to drop more and the rate of inflation-adjusted interest to increase more, and so on.
This is why the ECB is so desperate to boost inflation today so the trap doesn't set in tomorrow. Deflation is the wolf at Europe's door and the ECB is right to do all that it can to fight it off.