In Russia we currently have 11% of Central Bank's interest rate and you can get credit in commercial bank for about 25% in year. Why are interest rates so high?
I think the answer to your question does not require reference to economic theory as you are trying to understand why Russians cannot borrow at low rates. The prevailing high rates are not there for suppressing business activity, etc. This is something to do with the risk appetite of Russian commercial banks when dealing with domestic businesses.
Why are Russians facing rates as high as 25% when the base rate is 9%?
Central Bank's current base rate is 9%, also called repo rate. This rate is the main monetary tool used by CB to influence the interbank interest rates and the interest rates for loans, mortgages and savings. As you can see, the CB rate is low, but the commercial banks are adding huge premium (here it is 16%) to the base rate when lending to domestic businesses. Perhaps, they may face high default risks, political risk, high inflation, exchange rate risk, etc.
As a side note, this is a typical characteristic of a transition economy, that's said, Russians will face relatively high interest rates till they gain 'developed' status.
Answering the questions on the title, high-interest rate of the central bank (or increasing the policy rate by the central bank) means that they are trying to suppress the economic activity in order to avoid high inflation. In most of the countries, the purpose of the central bank is to stabilize the price fluctuation. When they increase its rate, it will move other interest rates through financial agencies' activity. Higher interest rate can prevent firms to borrow more, thus the economy might become sluggish.
As for your remarks about banking rate, there are two things to mention. Firstly, interest rate depends on its duration. Usually longer the duration, higher the interest rate. The policy rate is usually a very short one, so it might be natural that the policy rate and bank rate differs. Second, the policy rate can be to some extent thought as a risk-free rate while banking rate might include risk premium of that bank. This is why the bank rate is higher than policy rate.
A conventional answer would be that interest rates represents the rate of return Russian banks agree upon to lend money to physical clients/enterprises. If you believe this, you can create the following explanations. Two things come to my mind.
Option A: High Costs
Russian banks are unproductive and poorly managed. Their operational business is so inefficient that forces the bank to add a high premium on the interest rate.
Option B: High Risks
Russian banks have to lend money to clients with high risks. What would you do as a bank if you face many clients with high risks? You charge a higher price so in case somebody fails you may cover the sunk costs by revenues generated from credits to other clients. This is a simple way to `compensate' for uncertainty.
You can have a combination of two of course and that could already explain some of the differences you observe in the world and in Russia as well. Note for instance, that financial sanctions decreased stability of the Russian banks in a number of ways: a) enterprises (thus lenders) do not have access to external finance anymore and given the record low interest rates in Europe it means less access to cheap finance b) banks cannot finance on the external market themselves; thus if you have a liquidity problem you have less sources to take finance from.
This is not the end of the story however, as banks usually differentiate the interest rates they charge depending on the type of product they offer and a type of client, who wants to lend. If they do a poor job at differentiating between good and bad borrowers, another option arises:
Option C: Banks do poor job at separating the wheat from the chaff // Signalling does not work
Imagine you have two type of borrowers: risky and non-risky. If you would have perfect information on everyone, you could easily charge interest rates according to how risky the business of clients is. Lower rate for a risk-free guy, higher rate for a risky guy. But reality is more complex: you do not know for sure. And here they sit and show their documents, balance sheets, profits and loss statements etc both giving an impression how brilliant their business is. Yet if you know (post factum) that half of you clients go bankrupt, what do you do? Well, you just charge a high interest rate for both of the guys! Maybe it will be the wrong guy who will take your loan in the very end but at least you'll get high interest payments before he goes bankrupt. Maybe it is exactly the case with Russian banks. That is, maybe they just do a horrible job at investigating how reliable business of their lenders is. That indeed might be the case because many of Russian banks expanded their business in mid-2000 on the boom of the consumer credits. And it is not a heavy job to do: broad consumer base, high diversification - just give money to everyone and be happy. Yet now, when income stagnates, the business model does not work that good anymore. What do you need to do? Well, you need to start working with the enterprises. But lending to them is more complicated if you want to know for sure: you need knowledge of how business operates, what business-risks are relevant, how responsible is the team, how the industry feels in general and the list goes on. Maybe most of Russian banks do not know how to do it good and therefore keep charging high interest rates.
A Little Sidenote
Keep in mind two things however: a) My answer comes from the micro-perspective. The macro guys would probably point out on the issues related to capital flows and macro regulation, b) You better be clear which numbers you are reffering to and where do they come from. I've just checked the web-site of Sberbank. The web-site reports the following borrowing rates (minimum interest rate charged per annum): consumer credit (12.9%), morgage for flats in built houses (8.9%), security-free SME loan (17%), securitized SME loan (14.52%), SME loan for investment purposes (12.2%). Yes, these are minimal rates meaning that the actual rates are higher. But note two things: they are very far from 25% you mention (and I bet that the rates in private banks have to be lower if they want to compete with Sberbank) and there is a high variation between them: the maximum difference is around 8%. And we are talking just about one bank.
Thus, when you claim that the interest rates in Russia are way higher than in other developing countries you have to be sure that you compare apples with apples. And that you compare the averages of the apple sizes in both cases and do not take the maximum size on one side and the minimum size on the other. Hopefully you will find some of my explanations trustworthy ;)