It isn't necessarily the case that any particular cell "characterizes" the relationship. That isn't what you're doing. The chi-squared test for independence checks to see if the two variables as a whole are associated. It is slightly improper to think of a single cell as unrelated / distinct from the other levels of a given categorical variable, or that that cell is where the association 'exists'. However, it is perfectly reasonable to want to know which cells diverge the most from the counts you would expect under independence and thus contribute the most to the significance of the test. I'm pretty sure that's what you're asking. Bear in mind that if one cell is higher, (an)other cell(s) must be lower to compensate, so in some real sense the effect must exist in multiple cells.
@ArunJose and @Scortchi are correct that Pearson residuals are typically used to examine this. It may be helpful to visualize them, though. A way to do that is to use a mosaic plot that colors the cells based on the residuals. Here is an example using your data, coded in R:
d = read.table(text="stuff Fishermen Farmers Traders Craftsmen
positive 21 20 17 16
negative 15 23 43 15", header=T)
tab = as.table(as.matrix(d[,2:5]))
rownames(tab) = d[,1]
names(dimnames(tab)) = c("Schistosoma", "Ocupation")
# Schistosoma Fishermen Farmers Traders Craftsmen Sum
# positive 21 20 17 16 74
# negative 15 23 43 15 96
# Sum 36 43 60 31 170
# Pearson's Chi-squared test
# data: tab
# X-squared = 9.8257, df = 3, p-value = 0.02011
# Schistosoma Fishermen Farmers Traders Craftsmen
# positive 1.3462838 0.2964026 -1.7840859 0.6821634
# negative -1.1819983 -0.2602329 1.5663759 -0.5989198
What we see here is that, although you have a significant association, none of the cells strongly deviates from independence. The discrepancy is fairly similar in absolute magnitude in all cells. You can look at the residuals, calculated above, to get the actual numbers.
The plot also shows that traders have the lowest proportion with Schistosoma, whereas fishermen have the highest.