Local SEO is the work of making a business show up when people nearby search for what it sells, in map results, the local pack and searches like "near me" or "service plus city." A local SEO package bundles that work into a defined set of monthly tasks so you know what gets done and when.
Search engines usually decide local results based on three things: relevance (how well your listing matches the search), distance (how close you are to the searcher) and prominence (how well known and well reviewed your business is). You can't change distance. Local SEO works on the other two.
Here is a concrete example. Someone in a residential neighborhood types "emergency plumber open now" into their phone. The plumbers that come up in the map are typically the ones whose Google Business Profile lists the right category, accurate hours and the service area, whose name, address and phone number (NAP) match across directories, and who have recent reviews.
Local SEO is different from general SEO. General SEO aims to rank pages for searches made anywhere. Local SEO focuses on a specific area, so it adds tasks like business profile management, citation cleanup and city or service-area pages.
For most storefronts and service-area businesses, local search is where buying decisions happen, often on a phone within minutes. Our SEO services overview explains how local work fits with wider search work. If you already know what you need, you can compare local SEO packages.