Biology Standard Deviation Question

what does it mean if the standard deviation value increases with the independent variable?

Well you should give some context to what you're asking.

As far as I know for Biology AS (and A2) concerning standard deviation you should know (from the top of my head) :

1.SD gives a measure of reliability of the data collected. The less the value the greater the reliability. The more it increases the more varied and unreliable the data is getting.
2. About 60% (68%) of the values lie within 1 SD away from the mean and about 90% within two.
3. When the SD is large enough that it suggests that data of one set overlaps the other then the data collection and evaluation is very unreliable.
4. To indicate the SD in graphs you draw a vertical bar like an I showing all values between one SD (60%) from the average.