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In this article, the article discusses fidelity marking down the value of tech startups.

Based on context, it seems like somehow Fidelity has magically reduced the value of the startups, but this does not seem to make much sense, since Fidelity does not control the operations of the startups at all.

What does marking down actually mean in practice, and why is it important?

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There is no magic involved, merely a change in Fidelity's analysts' expectations of the future profitability of some startups.

The current value of a firm (as some other posts indicate) is the net present value (NPV) of all of its future cash flows plus the book value (the value of the company if it were immediately wound up). Future cash flows depend on the economics around the firm in the long distant future, particularly demand, growth in demand, the firm's ability to fulfil demand at the correct price (including price elasticities of demand), and interaction with any competition in the market. Fidelity's analysts have looked at their models and understanding of these underlying factors and decided that the NPV is likely to be lower than they had previously stated so they have reduced the stated value of the startups as reflected on their books.

I am speculating somewhat here, as an aside, but it seems likely that Fidelity felt that the startups' in question had too high expected growth given the current state of the world economy. A reduction in expected growth rate reduces all future cash flows and is likely to be more pronounced on profitability as fixed costs are pretty much already sunk. This is partly speculative but hopefully gives some "market colour" to the answer.

You also state that

Fidelity does not control the operations of the startups at all.

which is not true in many of these cases since these are mostly privately held companies; it is probable that Fidelity is one of, if not THE, largest investor in that company. If Fidelity decided to remove some of its investment capital it would be disastrous to the company and would pretty much make them insolvent unless another significant investor could be found. This gives them a significant presence on, and power over, the boards of these companies.

In all it is likely that this write down was done to reflect the fair value of the companies as going concerns given a complex set of economic parameters.

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