How is investing different from savings?

As mentioned before, savings is the amount left after meeting expenses and investment is done out of the savings made to meet future uncertainties or obligations.

While money kept in savings bank accounts will give interest, investment in mutual funds or any other dynamic investment avenue which is a blend of both equity and debt will give a value for money (read that investment can lead to growth of capital). This is where the main difference between savings and investment lies.

Also, while investments lead to wealth creation, savings is merely liquid cash. 

Why should one invest / why planning for investments is necessary?

You should invest to get the required sum of money for any goal at the correct time. In other words, if you want to achieve your financial goals in life like creating an emergency corpus, retirement corpus, children education corpus etc. then you must start by making an investment plan which will guide you step by step as to how to achieve your goals.

You cannot expect to achieve your financial goals by following blindly the experience and products embraced/practiced by the previous generation. Cost of major milestones have risen manifold in the last 25 years with the growth of Indian economy (read high inflation). There is a good chance of funds shortage as and when your goals come up if you don’t have an investment plan in place right from the beginning.