Institutions refers to a nations laws and legal system that protect individual and private property rights that promote private investment investment, and government and bureaucracies that provide infrastructure, education, regulation, etc. All of this is thought to be critical to development and most poorly performing economies can be described as having weak institutions.
Though it makes a lot of intuitive sense, it is a very hard thing to isolate in an empirical study. The problem, of course is that institutions and growth are very highly correlated, but is it good economic performance that accounts for the strong institutions or is it the strong institutions that created the preconditions for the strong growth? It is yet another case of correlation vs. causation.
In order to try and identify the causal link between institutions and development, you need to find a variable that helps explain the institutional quality of a country but is not correlated with the unexplained variation in growth. This is hard to do.
Three economists, Daron Acemoglu, Simon Johnson and James Robinson, wrote a seminal paper a few years back that did exactly this. They used settler mortality data to identify countries that were more and less hospitable to european settlement during the beginning of the colonial era. The idea is that in countries where settler mortality was relatively low, colonizers were more likely to set up more long term or more permanent institutions (England in the US, Australia and India for example), in countries with high settler mortality rates the incentives were to set up a minimal institutional architecture, extract resources, and get out (Belgium in the Congo and more generally tropical countries had more diseases). Of course the story doesn't work if the mortality rates are the same in the local populations, but in general those populations had become resistant to the local diseases and it was mainly the Europeans that were susceptible to these illnesses.
They use this disease climate variable as a determinant of the development of good institutions (while controlling for many other observable, like for instance, the nationality of the colonizer) and argue fairly convincingly that this settler mortality is unrelated to the
unobserved unexplained variation in subsequent growth rates. Their findings are robust: good institutions are important for good development.
So where does Haiti stand in this study? Its settler mortality was in the middle and fairly average for the Caribbean, but it was colonized by France and there is some evidence that this is worse than being colonized by England or Spain as were other more successful Caribbean economies. But the kleptocratic Duvalier reign in Haiti was probably the most damaging aspect of Haiti's 20th Century growth.