What are the potential consequences if the human population continues to grow at its present rate unchecked?
Mainly the exhaustion of our resources.
This question is very difficult to answer because it involves so many factors but I'm mainly going to focus on resource use. Let me know if I don't answer your question in the way you wanted to know.
Ever since the industrial revolution people have been living longer and healthier lives for the most part. With the revolution came advancing medicine as well as electricity, sanitation and distribution methods never seen before. This is what ultimately allowed the population to reach its current level of over 7 billion. This dramatic increase in population leads to an increase of consumption by all those new people.
The Earth itself has no problem fitting 7 billion people on the surface, but we all require a lot of materials and space to live which is the problem. To make room for all the people we've been destroying habitat. We sort of need to do this because we need more room to grow our food as well as make new stuff for all those new people. Eventually we'll reach a point where we can no longer grow enough food to sustain the population and this is called carrying capacity.
The main problem people focus on today is if we'll reach carrying capacity before or after we do irreversible damage to the natural habitat on Earth. Eventually, if the population gets to large, humans will consume to the point where the Earth will no longer be able to replenish the resources were consuming. Think of it as you have 10 apples. Every day you eat two apples and someone gives you another. Since you're consuming two apples everyday and only receiving one to replenish your stash, you'll eventually run out of apples. This is the same principle behind what is happening on Earth.