Why note the solvent level on chromatography paper when it is removed from the chamber?
Building on my comment, marking the distance that the solvent traveled allows us to calculate the retention factor $R_f$ (or apparently retardation factor, according to IUPAC meddlers who need to rename things with perfectly good names that everyone else uses). The retardation factor is the ratio of the distance traveled by the spot to the distance traveled by the solvent:

$$R_f=\dfrac{d_{spot}}{d_{solvent}}$$

If you are only performing one thin-layer chromatography experiment (TLC) ever, then you may be okay not marking the solvent distance. Since everything is on one piece of paper or one plate, you can compare readily:



From the above TLC picture, we can easily tell that unknowns A and B are probably the same compound as the standard, but unknown C is something else.

Now, what if we have two TLC plates/papers?



We can draw the same conclusions about the relationships between standard 1 and unknowns A, B, and C. Likewise, we can make some conclusions about the relationship between standard 2 and unknowns D, E, and F. However, we cannot easily determine if unknown F is the same compound as unknown A.

Determining the $R_F$ value lets us do that. Using the same solvent system, the distance traveled by the solvent and the distance traveled by a compound are both proportionally related to the length/height of the plate/paper. The solvent can travel twice as far on a paper that is twice as long. It turns out that the compound being analyzed also travels twice as far on a paper that is twice as long. The the ratio, $R_f$ is constant.

Let's drop in some numbers:



Now we can calculate the $R_f$ values for each spot:



After calculating the $R_f$ values, we can make some conclusions (assuming there are only two compounds in the entire experiment):


Unknowns A, B, D, and E are the same compound as Standard 1.
Unknowns C and F are the same compound as Standard 2.