The "tail" in tail risk referes to the tails of a probability distribution. A normal distribution has "thin" tails. The probability of huge outliers is pretty low.

If you have tail risk, then it means you have a decent chance of losing a lot more money than the typical variation. Your returns might look like +1.1, +0.9, +1.2 +1.05, -3. So your profit is pretty predictable with little variation, until suddenly you lose a lot of money.