Like blog posts, a Page can have an “Excerpt” field to override the automatic excerpt of 55 words from the beginning of the content. However, many themes don’t display this field when editing pages, so you can’t edit it.
This extremely simple plugin forces page excerpt capability “on”. The Page excerpt is visible in internal search results and “Query Loop” blocks, as well as in the output of many plugins (e.g. CC Child Pages). So I generally do want to decide for myself whether to accept the default excerpt.