If you started noticing it recently, then we are extremely glad that we added SD settings on the pay-off graph.
As Karthik Rangappa says in Varsity, Standard deviation lays down a very basic foundation for a quantitative approach to markets, which is very different from the regular fundamental and technical analysis thought process. Standard Deviation helps by showing you the upper and lower end range for the likely movement of the underlying and helps with the probability of it trading within the range and outside the range.
As the Settings suggest, we have 2 modes:
1. Fixed SD: This will show 1 SD and 2 SD ranges for the selected number of days. For example, if 5 days is selected, then it will show the standard deviation range of the underlying movement in the next 5 days.
2. Dynamic SD: This will show 1 SD and 2 SD ranges as per the target date and time selected. In this, if you select the expiry day as the target date, it will show the standard deviation range of the underlying movement till the time the options expire.
We also show the absolute values of 1 SD and 2 SD at the bottom right, besides Greeks.
Theoretically, there is a 66% chance that the stock will stay between +1SD and -1SD limits on your target day, and there is a 95% chance that it will stay between +2SD and -2SD limits on your target day.
If you are keen on understanding how 1 SD and 2 SD are calculated, there is a great article about it on Varsity here.