What it is
Palm oil is a vegetable oil pressed from the reddish pulp of the fruit of the oil palm, Elaeis guineensis, a tree grown across the wet tropics. There is no animal anywhere in that sentence, and that is the point: by the straightforward definition of veganism, a food or product whose fatty ingredient is palm oil is vegan. It is also nearly everywhere, because it is cheap, stable and semi-solid at room temperature, which suits it to baked goods, pastry and other ultra-processed foods as much as to soap, shampoo and cosmetics; by one estimate about 70 per cent of personal care products contain something made from it. So if the only question is whether palm oil is an animal product, the answer is a clean no. The reason it lands on a problem-ingredients list for so many vegans has nothing to do with what it is made of and everything to do with how it is grown.
The asterisk: why many vegans still avoid it
For a lot of vegans, the whole point is reducing harm to animals, and palm oil sits awkwardly with that even though it is plant-based. The oil palm grows best in precisely the warm, wet band that holds the world's richest rainforest, and clearing that forest for plantations, above all in Indonesia and Malaysia, which between them supply most of the world's palm oil, has driven serious habitat loss. The animals most often named are the Bornean and Sumatran orangutans, both pushed toward extinction as their forests shrink, along with the Sumatran tiger and the Sumatran rhinoceros; draining the carbon-rich peat soils to plant also releases a lot of greenhouse gas. The usual remedy offered is certified sustainable palm oil, overseen since 2004 by the Roundtable on Sustainable Palm Oil, whose logo is meant to mark oil grown to agreed environmental and social standards, though it is only fair to add that critics and some satellite studies have found certification is no guarantee against deforestation. So this one is a values call rather than a dietary one: palm oil is vegan, and whether you buy it, avoid it, or hold out for the RSPO logo is a judgement each person makes with their eyes open.