Why does K+ have more concentration inside of the cell compared to outside of the cell? Why is Na+ and Cl- the opposite?
Why nature has done it this way around is difficult to explain. What is certain, however, is that the membrane potential which results from the imbalance of these ions across the membrane is used for a variety of purposes, such as transport of other ions and molecules, action potential generation in neurons among many other things. 

How it is accomplished is mainly through the Na+,K+-Atpase pump and secondarily through Cl- channels that exchange Na+ for Cl- to lift the amount of Cl- outside the cell.