It is borrowed from computer programming: it means that the item on the left hand side is being defined to be what is on the right hand side. For example,
means that y is defined to be 7x+2.
This is different from, say, writing
where we are saying that the two sides are equal, but we are not defining “1” to be the expression “sin2(θ)+cos2(θ)“.
Basically, some people think that there should be notational difference between saying “I define
blah to be equal to
blankety” and saying “
blah is equal to
blankety“. So they use
:= for the first and
= for the latter. Usually, it is clear from context which of the two uses of the equal sign is intended (often because of signal words like “Let”, “We define”, etc.)