What exactly is SOLR? It seems like a magical technology that can

Do spatial search
do full text search

The problem is,

It doesn't say where does it store all the data. Does it have it's own proprietary database

If it store it's data in mysql, for example, I know that mysql cannot do spatial search well how can something build on top of it can?

Then someone said they use solr with mongodb. So solr can read mongodb and mysql? Who writes the glue? We?

Ultimately, what is this?

Database?
Index database?
API interface?

What is SOLR?
Solr uses lucene to do the spatial and full text indexing, not mysql. It basically wraps a REST-style service on top of lucene's index library so you can access it as a service. The wikipedia article is pretty good for an overview: http://en.wikipedia.org/wiki/Apache_Solr

An alternative to Solr that also uses lucene is Elastic Search, which I think is superior in at least a few ways--see this answer from the creator of Elastic Search: https://stackoverflow.com/questions/2271600/elasticsearch-sphinx-lucene-solr-xapian-which-fits-for-which-usage/2288211#2288211