Colloquial expression usually referring to arthropods.
The term "bug" has multiple meanings. In horticulture, it is typically a colloquial expression referring to arthropods, especially insects.
Colloquially, it can also be used to refer to microbes (micro-organisms). This meaning is discouraged here.
Entymologically, a "bug" is a specific sub-order (Hetereoptera), the so-called "true bugs". This sub-order contains about 40,000 species, in the order Hemiptera of insects. Example Heteroptera include bed bugs, leaf-footed bugs, seed bugs, pond skaters, and stink bugs.
When referring to "bugs" in a question (eg. "How do I remove this bug?", "What is this bug?"), try to be as specific as possible. For example, if it is a spider, use spiders and not bugs.