What ideas does Russell express in his essay "Philosophy and Politics"?

In "Philosophy and Politics," Russell shows how philosophy and politics have informed each other in nearly every culture. For example, communist leaders in the Soviet Union relied upon Marx's philosophy of history (historical materialism) to implement their version of communism. Russell argues that since politics and philosophy inform each other, a philosopher or a politician should seek and use the best philosophical/political perspective; and that perspective should be based upon empirical (observational) evidence on how to best provide for an ethical and happy society. Subsequently, Russell argues that a government that bases its practices solely on an ideology (often an abstract ideology) is too focused on an abstract ideology, effectively ignoring real practical applications of a philosophy and/or political agenda. 

Russell notes that while Hegel's (and Marx's) ideas seem scientific (based on the dialectic and both purported to be philosophers of history), those who have implemented their theories have done so with an "ends justify the means" ethos: 

If you know for certain what is the purpose of the universe in relation to human life, what is going to happen, and what is good for people even if they do not think so; if you can say, as Hegel does, that his theory of history is "a result which happens to be known to me, because I have traversed the entire field" - then you will feel that no degree of coercion is too great, provided it leads to the goal. 

In other words, if a person/group/country agrees with a government/autocrat/dictator simply because that government or leader claims to know what's best, then they will necessarily agree with any means by which to achieve their government's end goal. This is dangerous territory because it allows the government/leader to do anything. Not only is this dangerous; it tends to place too much importance on the big theoretical ideas, rather than addressing the real needs of the people. 

This is why Russell advocates empiricism or democratic socialism because he favors a political-philosophical perspective based on the social good, will of the people, and a perspective that is scientific (empirical) rather than theoretical. Russell's approach is inductive. 

What is the connection between Philosophy and Politics according to Bertrand Russell's essay?

Russell argues that throughout history, the politics of a culture can influence its philosophers and the reverse is also true, that the philosopher(s) of a given epoch and culture can influence the politics of that given epoch and culture. 

Russell notes that the Catholic Church is linked to the thinking of St. Thomas Aquinas and that the Soviet government was linked to the philosophies of Karl Marx. In the case of communism in the Soviet Union, those leaders (Lenin, Trotsky, Stalin) relied upon Marx's ideologies more than using empirical (scientific) analyses in determining the best government and social program for the Soviet Union. Russell argues that a government or governing body that relies too much on an ideology, and not enough on empirical observations, will necessarily fail in terms of efficiency and in terms of creating an ethical and happy society. 

Russell concludes that empiricism is the best philosophical perspective from which to advise politics because it is based on real scientific evidence (sociological, biological, psychological, etc.). Russell believed that a government that relies too heavily on an ideology is destined to use force to implement that ideological framework and force is usually required because the ideology might not conform to the real, empirical needs of a given society. Consider the Holocaust, burning people at the stake, and relocation under communism. Russell argues that ideologically-based governments use the "ends justify the means" in implementing their agendas; hence all the atrocities that have been used by some governments (Nazis) in hopes of achieving some more favorable end. Citing this example, the "ends justify the means" is a delusional and unethical way of enforcing social policy. Therefore, Russell shies away from any ideology that is, like the Nazi program, functionally unethical (even evil) no matter how (and why) they might justify themselves. When a government relies too much on a given ideology, to the detriment of their own people (or supposed enemies), clearly that ideological perspective ignores the happiness and actual needs of its people. A more scientific (empirical) perspective is more ethical and useful because it addresses the actual needs of the people without having to conform to some abstract ideology. 

Russell adds that an ideology is too absolute, too unchanging and narrow-minded. He favors democratic socialism or empiricist Liberalism as the most open-minded, scientific, and ethical philosophical program that should be linked to a political program: 

I conclude that, in our day as in the time of Locke, empiricist Liberalism (which is not incompatible with democratic socialism) is the only philosophy which can be adopted by a man who, on the one hand demands some scientific evidence for his beliefs, and, on the other hand, desires human happiness more than the prevalence of this or that party or creed.