how can potential barriers affect the projection of population growth?

Potential barriers? These would be world wars, new and unexpectedly virulent diseases creating pandemics, global warming raising ocean levels enough that significant portions of heavily populated areas are submerged (Bangladesh, China, etc.) and the resulting famine as large areas of farmland are submerged. Poor weather resulting in massive crop failures and the resulting starvation. Unexpected chemical or biological warfare by rogue nations.

One potential barrier could be weather related. Katrina and Andrew killed significant amount of people, so did the tsunami. That could skew the projection. Also gradually a lot of baby boomers will be nearing death for the next 20 years. I'm not sure if this answers your question.

it can affect it in many ways. Too many to list.