Is Poisson regression a good fit for this dataset? I am using a hurricane dataset (specifically the NDAM and Gender_MF columns):  
set.seed(100)
library(ggplot2)
library(rio)
url = "https://www.pnas.org/highwire/filestream/616321/field_highwire_adjunct_files/0/pnas.1402786111.sd01.xlsx"
data = rio::import(url)
data = data[1:92,]
ggplot(data = data, mapping = aes(x = NDAM, fill = factor(Gender_MF), 
       color = factor(Gender_MF))) + geom_density(alpha = 1/20, adjust = 1/2)


Both distributions are skewed and need transformation.
My aim is to fit a model and see whether Gender_MF explains the hurricane damage. 
So, I consider the NDAM as a count and fitted a Poisson regression as follows.
pois.reg <- glm(NDAM ~ factor(Gender_MF), family = poisson, data = data)

The summary output

Does this Poisson regression model have a good fit for these data? How can I interpret the coefficients? Can I say Gender_MF explains the hurricane damage? 
 A: I'm ignoring external context about this paper and analysis for the purposes of this answer. 
1. Does this Poisson regression model have a good fit for these data?
We have no way to judge that from the output you have presented. 
2. How can I interpret the coefficients? 
I don't know which genders 0 and 1 represent. But the output means that 
Gender_MF = 0 has an expected NDAM of exp(8.936) = 7600 
Gender_MF = 1 has an expected NDAM of exp(8.936 - 0.068) = 7100
So Gender_MF = 1 is associated with a 500 unit decrease in NDAM relative to Gender_MF = 0. 
Could be worth your time to read How to interpret coefficients in a Poisson regression? 
3. Can I say Gender_MF explains the hurricane damage?
I would say instead that Gender_MF is associated with hurricane damage in this dataset, conditional on a set of assumptions that we cannot evaluate from the model output alone. 'Explains' is a bit ambiguous but hints at a causal claim, and I would be very wary of making causal claims based on this alone. 
