A conservative estimate is one that is cautious to avoid excess in approximating the quantity, degree, or worth of something. On the other hand a liberal estimate would be one that is cautious to avoid underestimating the quantity in question. For example a conservative estimate of the number of Buddhists in China is about 500,000,000 whereas a less cautious liberal estimate is 1,200,000,000. 
Josh Becker, the film director, described the definition of a conservative estimate as "'the low point'" continuing "Whereas, a 'liberal estimate' would give you the high end. Isn’t this simply a variation of the half-empty, half-full view of the world? Conservatives are on the half-empty side, and honestly, who wants to be there? The half-empty philosophy is the pessimistic, downbeat view, and ultimately anyone with that perspective is a drag to be around. Not only that, but 'the conservative estimate' regarding just about anything, from contracting work, plumbing, carpentry, car repairs, movie budgets, or anything else, is nearly always wrong. Estimates rarely if ever come out at the low-end. If I take my car in to have a squeak fixed, they’ll certainly find something else wrong, and the initial, conservative, estimate of $200, invariably becomes a reality of more like $1,000."