We are now in the 21st century where, as you all know, computers play a major role in our daily life.
Aviation has evolved from simple planes made out of paper and wood to modern airliners that can carry up to 800 people, with a range of 8200nm, at speeds of up to 450 knots (833 km/h) whilst cruising at 36000ft above the Earth. Computers were, amongst other things, major contributors to this gigantic evolution: they were used for designing efficient aircraft with new aerodynamic properties suitable for special roles (military, commercial etc) but are also used to 'fly' the larger jet airliner aircraft, calculate cruising altitudes, speeds, weights, efficiency as well as many other things.
A modern airliner relies on computers in order to keep it 'flying' which poses a scary thought: what if these computers fail? Redundancy; airliners may have 2 or more computers for back-up purposes in case of a, unlikely, failure. Nevertheless, these failures are, statistically, very rare and computers have made flying much safer than it ever was, using methods like TCAS (Traffic Collision Avoidance System) which prevents mid air collisions.
Also, computers are used for 'simulation flying' where pilots can practice their emergency skills, checklists, operations etc. It is possible for a pilot to have 'zero flight time' in real life: 100% of his flying has been on simulators and has never flown in real life until his/her first commercial flight. This means that pilots do not have to fly in a 'real' aircraft to learn how to fly, which is both safer for people (if, for some reason, the aircraft had an engine failure in a training flight people on the ground would be put at risk) and is much more ecological as a simulator does not run on kerosene.
From an Air Traffic Control point of view, computers allow the mass numbers aviation traffic to pass from country to country at very efficient and safe speeds. It is a common misconception that the sky is huge and mid air collision are rare; without computers in aircraft systems and air traffic control centres, flying would be very dangerous as there would be vast amounts of traffic in the same airspace (in the vicinity of a major airport, for example), making collisions highly probable.
Looking at the commercial side of aviation, computers have allowed an uncontrolled boom in air travel. It is now simpler than ever to book a ticket to almost any part of the world through a click of a mouse in your home. This has created a, sort of, 'global network', where anyone can choose where to fly to for holidays.
In conclusion, computers have allowed the evolution of aviation to increase in a very short period of time and increase the safety of flying in general.