Compote has two meanings as far as food is concerned. It can be a dish that you eat, or, a dish that you put food into.
As something you eat, it is a dessert of fruit, fresh or dried. It can be a single fruit or a combination of fruit. The fruit is usually kept in a chunky form, as opposed to being mashed. The fruit is stewed or baked in a light syrup. The syrup can be spiced and / or have alcohol added to it for taste.
A compote can be used as dessert or breakfast; it may be served on its own in a dish, or used as a topping for another dessert.
It is usually served room temperature or chilled, but nothing says it can’t be served warm in the winter.
A compote can even be fermented: a rumtopf is a form of compote. Compotes allowed to sit with alcohol in them won’t ferment, because the alcohol content will usually be too high for yeast to live in. With no alcohol, though, either natural yeast or added yeast will ferment the fruit and create alcohol from it.
The word compote is also used to mean a serving dish with a stem for serving fruit in. The dishes also got used a lot to put out mints or sweets in for decoration and guests.