Up to my understanding, Indexing means visiting your site by Google search engines. Thus improves the page rank for your site. Whenever Google crawls your site thus improves back link and keyword for your site
Crawling is when a search engines robot 'bot' comes to your site and starts looking about at the information and browses for stuff to index. Indexing is when a page on your site gets put into the search index ( so its searchable ) Indexing is the part done after the crawling and is the bit when the search engine looks into what the crawler found and then finds what your page is about so it can be indexed correctly.
database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of slower writes and increased storage space. Indexes can be created using one or more columns of a database table, providing the basis for both rapid random look ups and efficient access of ordered records.
A Web crawler is a computer program that browses the World Wide Web in a methodical, automated manner or in an orderly fashion. Other terms for Web crawlers are ants, automatic indexers, bots, Web spiders, Web robots, or—especially in the FOAF community—Web scutters
Indexing is the process of sending a page to goggle and it is stored in the database where as crawling process in which search engine comes to your site and check the information on your site. Moreover when a website is loaded in a search engine it is called indexing and checking the information on your site by search engine and setting a page rank of your site is called the process of crawling.