It means something negative is happening very fast. It happens so fast that it causes us to be "alarmed" (nervous, scared, worried, etc.) The price of gasoline is rising at an alarming rate. The number of new cases of the the disease rose at an alarming rate. Teens are dropping out of high school at an alarming rate.

It can mean a rising, fast or escalating rate as in rising food prices.

Something that happens super fast. Often times it is negative, as the word 'alarming' suggests it is at least a somewhat negative situation.