In the United States many poorer States tend to be "Red States" while wealthier States tend to "Blue States". Is there any specific reason why this is the case?

The USA is fairly unique among nations in terms of the distribution of its cities across the country - this is more a matter of geopolitics than history, but you could say there are historical roots.

Most economic activity takes place in cities, so cities are wealthy. But, not all cities are made equal.

Many nation states have a history where political/cultural power was first consolidated in a "core territory" and then extended outwards (think: Muscovy, Paris, or Bangkok). The outlying regions had different cultural, religious, and sometimes linguistic heritages but over time they were assimilated (sometimes by force/purges) and economically integrated into the core (sometimes by expensive infrastructure projects). However, everything redirects back to the core. When a territory like Brittany becomes "French" over the course of the 15th-18th centuries, it's not like joining a union or confederation: it's a subordination to Paris. The preponderance of economic and political activity stays in the core, the primate city (a "city far above all other cities"). The phenomenon of primate cities is very clear when you look at for instance this population cartogram of France or this one of Thailand. Now you can see why, e.g., DeGaulle spoke of the liberation of Paris as if it were the liberation of France.

The USA does not work this way. We are a settler state and we have the good fortune of having the world's largest contiguous piece of good farmland, overlaid by approximately half of all the navigable inland waterways in the world, with a beautiful connection to the world ocean and overseas markets. One of the USA's first tasks was to settle and secure the Midwest. The Founders thought about this consciously. Here's Thomas Jefferson talking about the importance of the LA Purchase:

##There is on the globe one single spot, the possessor of which is our natural and habitual enemy. It is New Orleans, through which the produce of three-eighths of our territory must pass to market, and from its fertility it will ere long yield more than half of our whole produce and contain more than half our inhabitants.

Jefferson foresaw that the Midwest would become this huge, integrated economic region with trade and exports facilitated by the magnificently navigable (seriously, it's like it was designed) Miss-Oh-Missouri river system.

So all of this goes back to your question about "Red States" and "Blue States." Because of the specific settlement pattern of the USA, we have a relative abundance of states with regional cities. These cities were founded on the heads of navigation or the important points of confluence in the Miss-Oh-Missouri River System. For example, Cinci and Pittsburgh and St Louis are classic examples of these cities that grew up around the river trade and remain economic regional anchors today. These regional cities can "balance out" a relatively large and sparsely populated rural region, resulting in a swing state. If the regional city is too large, the rural areas simply get outvoted: Illinois is a good example of this. If a city gets lumped in with "too many" rural voters then it gets outvoted, as the reliable Democratic voters of Norleans get outvoted by their rural cousins. When they balance each other perfectly, then you get a so called swing state but always remember that this is talking about a moment in time. For example in 1997 (the latest we are allowed to talk about) Missouri was the bellwether swing state of the whole nation and voted exactly in line with the overall result in election after election, but, if I can skirt the rules, "then was then and now is now," nuff said.

The solid red states that are poor, that you're thinking of, are states that simply don't have a large regional city. They have mostly rural areas and a few sub-regional cities. An excellent example of this is Mississippi. The largest city in MS is Jackson, which is the 148th largest city in the USA - it's way down the chart.

If you were given liberty to redraw US State borders you could arbitrarily create "red" and "blue" states in any region of the country. It's just a matter of how much mashed potatoes (countryside) you put with your peas (cities).