How to read a chromatography calibration curve?
I assume your teacher explained the HPLC separation. If injected a mixture of four ions you will get four peaks. Each peak has an area, which is proportional to the concentration of the substance.

Imagine you wanted to determine the concentration of chloride ions in your tap water. What you would do is that you will prepare several known concentrations of chloride ions using $\ce{NaCl}$ solutions, say $0$ to $\pu{350 ppm}$ (look at your calibration chart). Inject them one by one, and measure the peak area, let us say the second peak is that of chloride ion. The peak shape is Gaussian in real work but you can &quot;estimate&quot; them as triangles. Recall triangle's area is very easy to calculate.
First step: Plot the peak area for concentration. What you get is a calibration curve.
The next step is to find a mathematical equation that fits this data.
Fortunately it is linear in your case of the form $y=mC$ where $y= \text{peak area}$, $m=\text{slope}$, $C=\text{concentration}$ in $\pu{ppm}$.
Now you would inject your tap water in the HPLC, you do not know the concentration ($C_1$) but you do know the peak area.
The last step is called interpolation. You go from the known area, and read the corresponding concentration axis. Viola! Now you know the chloride concentration in your tap water!
Alternatively, you use the equation, $y=0.1312C$, so I know the area of the tap water chloride injection, say, it was $\pu{40.0 units}$, so $C_1 = 40/0.1312 = \pu{304.9 ppm}$.
In typical tap water it is around $\pu{100 ppm}$, I just made up those numbers.
Bonus: Rationalize the units of the peak area on the $y$-axis! Why it is conductivity times minutes?