Why aircraft's fly at high altitude

Reasons:

1. Terrain clearance - As the land is not flat and has obstructions (man made or natural), to keep it clear of them aircraft need to fly high
2. Less Air resistance - Since air is thin at higher altitude, the resistance is less and it can travel efficiently and faster.
3. Low fuel requirement - As air is thin, the fuel air mixture needs to be leaned. This means that aircraft will get more performance with the same amount of fuel as it would have got at lower altitude.
4. Jet Stream - At high altitude above 30000 ft, the jet stream which moves at excess of 50kts (in winter it goes to 100kts or more) helps aircraft fly faster which are moving the same direction as jet stream i.e. it adds to the ground speed. Though travelling in opposite direction will reduce the ground speed.
5. Higher TAS and ground speed - Since less air at higher altitude the TAS is higher. This means that overall ground speed will increase.