The standard reply to this question is because fuel injection provided a better way to meet government fuel economy and emission standards, which is true. But equally important is the fact that fuel injection is an all-round better fuel delivery system.
Fuel injection has no choke, but sprays atomized fuel directly into the engine. This eliminates most of the cold start problems associated with carburetors. Electronic fuel injection also integrates more easily with computerized engine control systems because the injectors are more easily controlled than a mechanical carburetor with electronic add-ons. Multiport fuel injection (where each cylinder has its own injector) delivers a more evenly distributed mixture of air and fuel to each of the engine's cylinders, which improves power and performance. Sequential fuel injection (where the firing of each individual injector is controlled separately by the computer and timed to the engine's firing sequence) improves power and reduces emissions. So there are some valid engineering reasons as well for using fuel injection.
The earliest fuel injection systems were mechanical and were more complex than carburetors. Consequently, they were expensive and their use was limited. Chevrolet introduced a Rochester mechanical fuel injection system back in 1957, and it became the "hot" setup on Corvettes up through 1967.
The Europeans, however, were the real leaders in fuel injection technology. Bosch offered an early electronic system on Volkswagen Squarebacks in the late 1960s and early 1970s. By the early 1980s, almost all of the European auto makers were using some type of Bosch multiport fuel injection system.
In the mid-1980s, the domestic auto makers first turned to "throttle body" injection as a stop-gap system as they made the transition from electromechanical carburetors to fuel injection.
Throttle body injection is much like a carburetor except that there's no fuel bowl, float, needle valve, venturi, fuel jets, accelerator pump or choke. That's because throttle body injection does not depend on engine vacuum or venturi vacuum for fuel metering. Fuel is sprayed directly into the intake manifold instead of being siphoned in by intake vacuum.
A TBI fuel delivery system consists of a throttle body with one or two injectors and a pressure regulator. Fuel pressure is provided by an electric pump. It's a relatively simple setup and causes few problems -- but doesn't provide all of the advantages of a multiport or sequential fuel injection system.
The next step up from TBI was multiport injection. Engines with multiport injection have a separate fuel injector for each cylinder, mounted in the intake manifold or head just above the intake port. Thus, a four cylinder engine would have four injectors, a V6 would have six injectors and a V8 would have eight injectors.
Multiport injection systems are more expensive because of the added number of injectors. But having a separate injector for each cylinder makes a big difference in performance. The same engine with multiport injection will typically produce 10 to 40 more horsepower than one with TBI because of better cylinder-to-cylinder fuel distribution. Injecting fuel directly into the intake ports also eliminates the need to preheat the intake manifold since only air flows through the manifold. This, in turn, provides more freedom for tuning the intake plumbing to produce maximum torque. It also eliminates the need to preheat the incoming air by forcing it to pass through a stove around the exhaust manifold.
There are other differences between multiport injection systems. One is the way in which the injectors are pulsed. On some systems, all the injectors are wired together and pulse simultaneously (once every revolution of the crankshaft). On others, the injectors are wired separately and are pulsed sequentially (one after the other in their respective firing order). The latter approach is more complicated and requires more expensive electronic controls, but provides better performance and throttle response by allowing more rapid changes in the fuel mixture.