Let's call P1 the proportion of healthy in cluster 1 and P0 the proportion of healthy in the rest. The null hypothesis being tested is that P1=P0. The two-sided test will tell you whether there's a chance that P1!=P0, i.e. it's looking at the two tails of the distributions. With alternative = 'greater', you're only considering the tail of the distribution in the direction corresponding to P1>P0 and conversely, with less, you're only looking at the distribution in the direction of P1<P0. However before using a one-sided test, consider the cost of missing an effect in the other direction, i.e. do you only care about P1>P0 or is P1<P0 also of interest? As another example, imagine you're testing the effect of a treatment on patients. You want to know if the treatment is proving effective (e.g. P1>P0) so you may think of using alternative = 'greater' but in this case you wouldn't detect if the treatment is detrimental (P1<P0). Most of the time we don't know a priori the direction to expect and so I would recommend to do a two-sided test. Only do a one-sided test if the untested direction is irrelevant to the question you're interested in. For example if the conclusions you would draw are the same whether P1=P0 or P1<P0 then use alternative = 'greater' otherwise use the default alternative= 'two.sided'.