What is the relationship between population growth and economic growth? Population Growth is only one of several factors of influence on economic growth but it is not strictly necessary for the economy to grow.  I have also heard of the term called the population bonus - which describes how a change in the demographic breakdown in the working-age population can impact economic growth.

I want to understand what is the relationship between population growth and economic growth and how can population bonus potentially increase growth in GDP.   Can anyone help explain the importance?
This is actually quite complex issue. Taken narrowly answer to your question:


  what is the relationship between population growth and economic growth


Is that simply the relationship is positive. This is because in the question you ask only about growth of GDP per se. Growth ultimately depends on growth of production and labor is an important input in the most of production. One of the most widely used production functions is the Cobb-Douglas production function which has following form $Y = AK^{\alpha}L^{1-\alpha}$ and it is trivial to see that output depends positively on labor.

However, there are some problems with looking just at growth of GDP. Even though GDP will grow with more population you could in principle end up in a Malthusian trap. Yes GDP increases with more population but that is because we have more people and hence that does not mean that this increase in growth actually makes peoples lives better. This is why economists care not just about growth overall but rather per capita growth (that is economic growth per person). 

When it comes to the relationship between per capita growth and population literature gets more murky. The most widely used growth model is the Solow-Swan model and in it increase in population has no effect on per capita growth. In Solow-Swan model all growth is exogenously given by growth of technology. Most of professional macroeconomist believe in Solow-Swan model because there is quite a lot of empirical evidence in its support but in the last 30 years endogenous growth theory is challenging the Solow-Swan model.

In endogenous growth theory population growth can actually lead to also per capita growth. This is because in such models growth depends not just on exogenously given (predetermined) growth of technology but can be affected by choices society makes. One of those choices is also to devote more labor towards R&amp;D and knowledge development, hence in such model actually population growth can lead to sustained economic growth if that extra population is educated and channeled towards R&amp;D/knowledge creation. This being said an important caveat is that although endogenous growth theory got more popular in recent years and even Paul Romer got few years back Nobel Prize in Economics for his contribution to the theory, it is still not widely accepted because its extremely difficult to test. So take that as you will. 


  how can population bonus potentially increase growth in GDP


Population bonus is more widely known as demographic dividend. It referrers to situation where country's demographic structure improves in a sense that there are more working age people relative to either young or elderly. For example economy where you have 60 retirees 20 infants and 20 working age population will have (ceteris paribus) harder time providing for its people than economy where you have 10 retirees 15 infants and 75 working age population. This is because for most part all goods and services are produced by working age people (save some exceptions like child actors/paper delivery etc) and hence non-working age people do not really directly contribute to the economy.  Especially in those countries where state offers generous social benefits to non-working age people it is important to have enough working age population from which state can draw resources through taxes.

Thus having population bonus/demographic dividend can certainly increase GDP, if its sustained it can also lead to economic growth but it is worth noting that it is very difficult sustain growth this way. There is plenty of evidence that as people get richer their fertility declines and demography soon becomes unfavorable like in Europe or Japan. Hence, it is very unlikely demographic dividend can deliver long term sustainable growth but in can definitely help raise GDP while its happening and in principle can be sustained for few generations but not indefinitely.