Academic freedom isn't just about choosing what you work on (which was covered by the other answers). It also means that a researcher doesn't face consequences for what they research or for their conclusions, and the same for professors and what they teach (within the limits imposed by professional ethics, of course). In theory at least, if the conclusions of a study do not please whatever politician is effectively in charge (the minister for higher education or equivalent, or even above) or whatever private overseer, then the researcher/professor should not face consequences for this.
Think about for example an economics professor researching and teaching ideas that are not part of the orthodoxy, or an environmental scientist that reaches some conclusions regarding climate change that may displease an unfortunate fringe of politicians, or the same environmental scientist who finds that the actions of a powerful oil company (with friends in the government) are harmful, or a medical researcher who finds that some drug is inefficient / harmful, etc.
If lobbies had the power to influence politicians/private overseers who could fire professors and researchers at will, do you think there would be many studies who find that criticize the products/actions of big private companies? Of course, as you have noticed, funding for such research can be cut, which is a problem in itself.