Here is a complicated subject-- Annuities. You may have asked yourself what goes up when interest rates go up? Stocks and bonds usually go down so where do people put their money? Annuities is one answer. Annuties provide guaranteed income for life but you have to give up principal in return. You are transferring risk of running out of money to an insurance company by giving them the principal in return to a guarantee that the company will provide you steady income as long as you will live. If you die in one year, Insurance company keeps the money. If you live for 40 additional years then insurance company has to keep paying you money for 40 years. Annuities provide useful diversification tool for a portfolio and guarantees that you will get a certain minimum income for life. Annuities are similar to pensions where you get pension as long as you live.
So what is the connection between RBI interest rates and Annuities? Well, how much an Annuity pays depends on the prevailing interest rate at which you put your money into an Annuity. Since interest rates change, putting money into annuities is generally beneficial when interest rates are high. This is one reason why investors rush to annuities when interest rates go up. Every investor is running out of time when it comes to annuities. With retirement closing in, there are only so many opportunities every investor will get to invest in annuities. If you don't know what annuities are then you really are running out of time.
Here is an example of how annuity will work. Let's say you have 10 years to retirement and you invest

100,000 when RBI interest rate is 5%. Annuity interest rate will be computed as fixed rate + variable crediting rate + RBI interest rate. Since you will not be taking money from the annuity for next 10 years, your principal is allowed to grow

208, 835.60 giving you an income of

1,476 month for life.
Now, let's assume that interest rates go up to 7% in 5th year (beginning) and you decide to add another

100,000. The second investment will grow for six years at higher total rate (10.5%) while first investment will grow as the previous rate (8.5%). At retirement a weighted average rate is computed (9.38%) and you will receive

2, 916 / month for life. Keep in mind that this is a simple example because age is also factored in to estimate payout. Generally older you are you will get higher rate which would boost your income more than what is shown in the example.
There is a third option where a person waits till s/he retires and takes out all his money and invests into annuities. It may work well or it may not work well. For example, in our case the interest rate at the time of retirement is 2% giving an annuity payout interest rate of approximately 5.5%. Depending on how much principal grew in alternative investments, he may get higher monthly payments. Generally, it is risky to wait. You should always consider investing some part of your money into annuities when interest rates are high.
This concludes a general summary of annuities. The primary risk of annuities is that you don't want insurance company issuing annuity going bankrupt. Most countries have legislation that requires insurance companies to set cash aside for their annuity commitments making annuities very safe.
Indian annuities may work slightly differently. I have explained what is commonly known as fixed annuity. Their are variable return annuities where cash payouts for life get adjusted for inflation. Also, annuities can be bought for one life or two lives (husband and wife). Payouts for two lives is generally lower. There are other customizations. For example, you can buy annuity for one life with guaranteed minimum payout for 10 years. This way annuity will pay money to you as long as you live but if you were to die in one year since you began cashing the annuity then, due to guaranteed minimum payout of 10 years clause, your wife will get guaranteed money for 10 years before annuity stops paying her any money (because it was single life with 10 year guarantee). You may look at following sites for more info on Indian annuities:
Best pension plans in india ? Disadvantages and Advantages
Immediate annuity products getting competitive, but choose carefully - Moneylife