"Development policy needs to be about poor people, not just about poor countries." Please explain this statement to me in more depth so I can understand it.

The statement "Development policy needs to be about poor people, not just poor countries," carries a lot of baggage. Let's discuss what it means first and then discuss that baggage later.
Development policy is a package of assistance that's given to poor countries by richer countries, or by international financial institutions such as banks or the International Monetary Fund, or by agencies such as the World Bank or the United Nations Development Program. That assistance could come as cash or loans, tax breaks, or favorable terms in treaties. It could also come as help with large infrastructure projects such as building dams, creating fiber optic communications networks, building hospitals and schools, or funding public health initiatives.
When we say that development policy ought to be about people instead of countries, we mean that we should focus on what people in a country need, instead of simply prescribing remedies for a whole country. A country isn't anything without its people, so sending development aid which looks good on paper but doesn't really help anyone doesn't make sense. It's much better to send aid that can be targeted to specific people with specific problems.
That quote about people means focusing on policy outcomes, not the policies themselves. It's easy to say, for example, that a country that's having trouble repaying a loan should cut government payrolls in order to free up money to service its debt. If you focused your development policy on people instead, you might actually expand government payrolls to help raise incomes and increase consumption, thereby increasing government revenue. Actual policy is a lot more complicated than that, but you get the idea.
The baggage that accompanies the original quote goes something like this. Development which is brought to poor people from outside is fundamentally flawed because it denies them agency. Poor countries don't need saviors. They need money, but just giving them money, whether you call it people-centric development policy or not, won't help them in the long term. True development has to come from inside the country, even inside the people, because without the will to help themselves, any outside aid is lost on them. The catch-phrase which encapsulates this point of view is "trade not aid." If you really want to help poor countries, you would buy their exports, give them access to your markets, give them scholarships for their students to attend your universities, and share the patents of your medicines with them. Your original quote recognizes only two forms of something unhelpful. There's no room in it for the people, because "we" are doing something to "them" when we "give" them development policy.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.739.1444&rep=rep1&type=pdf

http://www.globalization101.org/trade-not-aid/

https://www.devex.com/news/q-a-how-rwanda-focused-pepfar-funds-on-people-centric-not-disease-centric-care-92918