A "spike" is something that's sharp and pointy.

If you're looking at a graph of numbers or statistics, and the numbers rise very suddenly, the shape on the graph also looks sharp and pointy. So when a number suddenly rises, we call it "a spike". 

Here are some examples:

There's been a huge spike in the number of deaths resulting from prescription drug overdoses.

We've seen a spike in customer complaints since we launched the newest version.