Fisher's exact test in 3x2 contingency table I have two groups of patients (A and B) with a congenital malformation which might present itself in 3 forms (a or b or c). 
Sample sizes are small as you can see, so I think the best test to check whether there's a statistically significant difference between the 3 forms in the 2 groups is a Fisher's exact test in a following 3x2 contingency table:
group A: 2 a, 12 b, 1 c
group B: 5 a,  3 b, 1 c

My question is: how should I interpret the p value? I don't understand what is that referred to. Having the p value, how can I say that one of the three forms is statistically significantly more represented than the others (if true)?  
 A: It sounds like you are asking a lot of different questions here.

My question is: how should I interpret the p value? I don't understand what is that referred to.

The null hypothesis for Fisher's Exact test is that the groups do not affect the outcome, i.e. that they are independent. Rejection of the null hypothesis indicates the outcome (a, b, or c) is dependent on group.
fisher.test(matrix(c(2, 12, 1, 5, 3, 1), 
            nrow=2, ncol=3, byrow=TRUE))
Fisher's Exact Test for Count Data

data:  dta
p-value = 0.05082
alternative hypothesis: two.sided

In this case your $p$ value is approximately 0.05082. I will let you decide whether to reject the null.

Having the p value, how can I say that one of the three forms is statistically significant more represented than the others (if true)?

This is a separate question and I'm not sure what you are trying to ask.
A: Totally agree with Ellis, the null hypothesis of the Fisher's exact test is that the outcome is independent from the groups. If rejected, it might be helpful looking at the observed frequencies and discuss such result in a broader context by integrating other sources of information. This latter could be your best shot as drawing solid conclusion with such a small sample size can be misleading.
