Beta phase in software development generally begins when the software is feature complete.
Taken from Wikipedia:
Beta (named after the second letter of the Greek alphabet) is the software development phase following alpha. It generally begins when the software is feature complete. Software in the beta phase will generally have many more bugs in it than completed software, as well as speed/performance issues. The focus of beta testing is reducing impacts to users, often incorporating usability testing. The process of delivering a beta version to the users is called beta release and this is typically the first time that the software is available outside of the organization that developed it.