A finite population is one where you can count a number up to a certain limit. A good example for this is at my job and if there was a project to quantify the average salary here in the workplace, you would have to add all the salary's up and divide it by the number of employee which is 18. When it comes to a infinite population its one where you cant count because thing just keep recurring. A good example for this would be how humans in the world are born every day, all you could probably do is gather details in samples like lets say how many baby's are born in a given year in the whole world. This would be one were you would have to make a judgement call based on samples.

I think that these to quantifying factors are important in statistics because of the fact that it can help with quantifying certain data that can be for a infinite population or for one that can be a finite population. I believe that this data that's collected can help in so many ways from how to run a efficient business or things that can help are climate and many more. Discuss with references