curl supports "chained" HTTP compression algorithms, meaning that a server response can be compressed multiple times and potentially with different algorithms. The number of acceptable "links" in this "decompression chain" was unbounded, allowing a malicious server to insert a virtually unlimited number of compression steps.
The use of such a decompression chain could result in a "malloc bomb", making curl end up spending enormous amounts of allocated heap memory, or trying to and returning out of memory errors.