It's a measure of how efficiently an algorithm works. It basically says the time taken is PROPORTIONAL to some function of n (the number of inputs). O(1) means it always takes the same amount of time no matter how much input you throw at it. O(n) means the time it takes to output grows linearly with respect to n. Same can apply to O(log(n)) and O(n^2).
Note that if you have a sum of different things, keep the one that grows the fastest and throw out everything else. O(n+1) becomes O(n), O(n^2 + n*log(n)) becomes O(n^2), and so on.
Another important thing to note is that we don't allow constant coefficients in Big O notation. We don't put O(3) or O(n^2/2). Those are supposed to be O(1) and O(n^2). It's only when the coefficient is related to n in some way, like in O(n*log(n)) for example, that we keep the coefficient. This makes sense when you realize that what Big O notation is saying is that the time taken is PROPORTIONAL to whatever's inside that big O.
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