What are the advantages of using Apache Solr over the core search module?
This article gives a thorough and straight-forward answer to your question.


  Performance improvements with Apache Solr
  
  High traffic sites running search queries against the database can start to degrade the site’s overall performance if the database becomes the bottleneck. This is also true for lower traffic sites with lots of content. Complex search queries can be slow to run.
  
  Requirements for features such as faceted search (see below) are becoming increasingly common. This can be delivered in conjunction with Drupal core search using the Faceted Search module but the inherent scalability and performance implications are well documented by the module’s maintainers.
  
   Other useful Apache Solr features
  
  Apache Solr also supports indexing and searching multiple sites (imagine internal intranet site and external corporate site), indexing attachments (eg PDFs, Excel documents) and recommended content blocks driven by a node’s taxonomy. The module page and the Acquia Search overview both have a good overview of the Apache Solr features that Drupal supports.