The lines which i have highlighted is what I want to be explained to me. This is with reference to indian economy
The private sector is households and companies. The public sector is the state and national governments. When the author says "private investment" they presumably mean non-financial investment like homes and educations for household members or business processes and software and factories for companies.
The money the private sector wants to save can go into "private investment" or a loan to the government. The more the government wants to borrow the higher the rate of return required by lenders. That rate is the interest rate.
In actuality a household buying a government bond can also be described as making a "private investment" but then it would not make sense to suggest there is "not enough left over for private investment". In order to make a sensible interpretation it is necessary to believe the "private investment" the author intends is non-financial (like a home or factory).