Operational amplifier (op-amp) is one of the main building blocks in electronics. First created in 1941 by Karl D. Swartzel Jr. The best definition can be found in the quote below:

An operational amplifier (often op-amp or opamp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output.[1] In this configuration, an op-amp produces an output potential (relative to circuit ground) that is typically hundreds of thousands of times larger than the potential difference between its input terminals. Operational amplifiers had their origins in analog computers, where they were used to do mathematical operations in many linear, non-linear and frequency-dependent circuits. The popularity of the op-amp as a building block in analog circuits is due to its versatility. Due to negative feedback, the characteristics of an op-amp circuit, its gain, input and output impedance, bandwidth etc. are determined by external components and have little dependence on temperature coefficients or manufacturing variations in the op-amp itself.

The ideal op-amp characteristics are:

• the V+ and V- inputs have infinite resistance
• there is zero current into and out of both V+ and V-
• if V+ is above V-, however slightly, then Vout will be Vs+
• if V- is above V+, however slightly, then Vout will be Vs-
• when V- is V+, Vout will be halfway between Vs+ and Vs-
• the gain of the amplifier is infinitely large
• when V+ and V- change by the same amount, Vout stays the same
• as long as in-/outputs are within Vs+ and Vs-, changes to Vs+ and Vs- have no effect
• the behaviour is identical for any frequency, temperature, and time span

Some really nice explanation for the above list can be found in Jeelabs