How do travel sites deploy meta search?Do they store all the data in their database or do they crawl other websites for information ?

No serious meta search engine uses web scraping, it's a very bad and short-term solution that will fall apart quite easily. Maintaining such solution is a nightmare, especially for serious metasearch players (e.g. Kayak, Momondo, http://Atlastravelengine.com, etc.) with many providers integrated into their engines. The only long-term solution is to integrate the travel websites into the metasearch engine through API or feeds. Yes, metasearch engines store some (not all) data in their database. This is required for performance and flexibility in the service.