Indexing is implemented at the feature level and each feature that supports search implements its own indexing. The indexing happens when content changes inside a feature instance not when it is newly added to a page, ie if you add an empty Image Gallery to a page it does not have content yet and nothing is indexed. Once you add content ie images it will index and it will also index the module title (it is not instantaneous it may take several minutes after editing before the content appears in search).
But the down side is that if you search on the module title each image in the gallery will be a search result since they all have the same title associated with the module and each image is represented as a separate indexed document in the search index.
See also Site Search Overview
Best,
Joe