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.