Other contributors have already tied this quote to criminality, and progressive concerns with big business and elite interests. This is certainly true (and a key theme of Progressivism in general), but it is also worth keeping in mind that Roosevelt could be deeply pragmatic in his policies. For example, take his reputation for trust-busting: his actual record revealed him to have been somewhat selective in terms of which big business operations he would prosecute, especially when compared with his successor Taft, who was far more active on this front than Roosevelt had been (and who, in fact, Roosevelt criticized on precisely that issue).

As far as the quote itself is concerned, I think that, more than anything else, Roosevelt is recognizing in it the role that education plays as a force multiplier in life. Certainly, education can prove to be a threat to the public welfare (this is a theme which other contributors have already pointed out), and this quote very dramatically expresses that notion. A criminal with a college education can do a lot more damage on a much wider scale than one who remains uneducated. But that same force multiplier applies to law-abiding citizens as well. To have a college education is to vastly expand the scope of one's opportunity in life. It can serve for the benefit of society, and to its detriment as well.

This quote is interesting because it doesn't, like people tend to do, attribute crime to poverty, but instead says that a person is normally a criminal because they have the nature of a criminal. The only difference between an educated criminal and a poor criminal is that the educated criminal has the potential and often influence to commit crimes that affect more people and then are therefore more destructive.

Some people seem to think that Roosevelt is putting forward the pessimistic view that man is naturally dishonest. However, on a more optimistic note, one could also claim that he is supporting the idea that poor people's opportunities are limited due to poverty and not to intelligence and other positive attributes linked to the educated classes.

Roosevelt is referring here to the robber barons, those captains of industry who used all kinds of underhand methods to consolidate their vast wealth and power. During his presidency Roosevelt took on the power of corporate trusts, including the railroad trusts, which he and other Progressives believed were unfairly driving smaller competitors out of business and then robbing the consumer blind because they no longer had any serious competition.

The robber barons who operated these trusts were, for the most part, from elite educational backgrounds. According to Roosevelt, this made them more dangerous than common thieves because they could use their superior intelligence, not to mention their wealth and political power, to steal more from the American public than a simple thief ever could.

Theodore Roosevelt was the first of America's three progressive presidents.  Because he was a progressive, he worried about the power of big business and the elites who ran them.  This quote shows this worry.

In this quote, Roosevelt is saying that people with college educations (who were relatively rare in those days) were more dangerous to society than those without.  He was saying that a person with a college education could exploit others on a much larger scale.

If you have no education, you can only steal by breaking into things, he is saying.  But if you are educated, you can use that education to steal in big ways.  You can use it, for example, like Bernie Madoff did and steal billions of dollars.  Or you can use it like a robber baron to make a monopoly and use that to steal from the the population as a whole.

So, what Roosevelt is saying here is very much in line with the progressive idea that elites were a danger to society.  He is saying that educated people can steal in bigger ways that are more dangerous for society (like Madoff or the Enron people) while the poor can only steal a little at a time.