This is a word of two parts.
'Giga' meaning a thousand million.
'flops' which is an abbreviation of 'floating point operations per second'. A floating point operation is a single maths calculation within a computer that uses decimal numbers.
e.g. 1.2 x 1.3 is a floating point operation.
Therefore, gigaflops means a thousand million floating point operations per second.
To show how much progress has been made, in 1976 a Cray 1 supercomputer, then the most powerful computer in the world, cost £6 million and was capable of only 0.13 gigaflops. Just 35 years later, a standard Intel CPU chip, that you can find within a modern personal computer, can do 42 Gigaflops for about £150. Four hundred times quicker than an early supercomputer!
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Click on this link: Gigaflops