From AEM documents I can figure it out how to write queries for Aem content search, but How search feature works in AEM? Which bundle or framework does the magic of searching the content and present back. How internally content is being traversed when I use search queries ?
AEM uses OAK indexes to implement the search engine. AEM repository is a database and like every other database, it needs indexes to perform speedy searches. You can read more on: https://docs.adobe.com/docs/en/aem/6-2/deploy/platform/queries-and-indexing.html
In general, you define indexes (in case OOTB indexes are not enough) under /oak:indexes node. These indexes, in a broad sense, contain list of properties and nature (async, full text, property, lexical rules) of index and the path to be indexed (or excluded from index).
AEM generates a lot of lucene index data in your repository and data store and that is used to quickly lookup the nodes for your queries. Whenever, a query is fired the AEM instance loops through the indexes and finds the index which will provide the results with least traversal cost. If no such index is found it will resort to node traversal which is normally bad for performance but has some limited edge case uses.
You can integrated Solr and ElasticSearch with your AEM instance to use other advanced features but that is simply an extension to the built-in engine.
Search and promote (which is more of an external search) is not related to internal index and is more like a site crawler.
Queries and searches is a very broad topic so I suggest you read this reply as a summary and more details can be found from the link above.