What are the advantages of the B747-8 airfoil over B737's airfoil?
The airfoil profile you've shown is called a supercritical airfoil.

Typical airfoil sections are curved on the top and the bottom. The airflow over the top of the airfoil is accelerated i.e. the airspeed over the top of the airfoil is more compared to the free stream velocity. The associated reduced pressure helping to create lift.


Source: www.symscape.com

From the figure, two things can be inferred:


The pressure over the upper surface is lower compared to the lower surface
The pressure gradient is favorable in the forward section of the airfoil (where most of the lift is produced), while the gradient is adverse in the rear half, which can cause boundary layer transition and possibly separation, if the gradient is too severe.



Source: code7700.com

For low speeds (and low angles of attack), this causes no problem in lift generation. However, most of commercial airliners fly at in the transonic regime (with speeds ~ Mach 0.9), the flow over the top of the wing may reach supersonic speeds even when the aircraft itself is flying at subsonic speeds.


Source:fluid.mech.ntua.gr

The speed at which this happens (flow over wings becomes supersonic) is called the critical Mach number. The flow decelerates through a normal shock wave, resulting in a severe adverse pressure gradient over the rear of the airfoil.


Source: fluid.mech.ntua.gr

This causes serious problems like:


The adverse pressure gradient over the shock wave causes flow separation, decreasing lift and increasing drag. The speed above which the drag increases significantly is called the drag divergence Mach number



Source: history.nasa.gov


As the speed increases, the shock wave moves to the rear, as does the lift producing region. This causes a nose down pitching moment and stability issues.



"Transonic flow patterns" by U.S. Federal Aviation Administration - Airplane Flying Handbook. U.S. Government Printing Office, Washington D.C.: U.S. Federal Aviation Administration, p. 15-7. FAA-8083-3A.. Licensed under Public Domain via Commons.

The supercritical airfoils are designed to overcome (or delay) these problems. Designed by Richard Whitcomb, the main characteristics of these airfoils are,


'flattened' upper surface
highly cambered aft section
smaller leading edge radius compared to the traditional airfoils (that is why they are so thin)



Source: aerospaceweb.org

The main advantages of supercritical airfoils are,


It increases the drag divergence Mach number. For example, in the F-111, the drag divergence Mach number was increased from 0.76 to 0.88, a 16% increase.
The shock waves are developed further aft when compared to the normal airfoils
They greatly reduce the shock induced boundary layer separation, reducing drag


The figure below shows a supercritical airfoil in a transonic flow. Note the location of the normal shock compared to the 'normal' airfoil.


Source: space.bas.bg

The supercritical airfoils were not available when the Boeing 737 was first designed. However, the 737 NG airfoil incorporates elements of supercritical design,as does the Boeing 747-8 airfoil.

The supercritical airfoils reduce the fuel required, as they allow the aircraft to cruise at higher speeds with lesser drag. Additionally, the Boeing 747-8 has a wing span of ~68 m, which gives plenty of storage space for fuel. Also, improvements in engines and airfoils means that the 747-8 has nearly 50% more range compared to the original 747-100.