I have a registration page on the site, when i clicked submit, generate a Lead record by trigger, but now does not work.
you might want to read salesforce's documentation on triggers
Apex triggers enable you to perform custom actions before or after changes to Salesforce records, such as insertions, updates, or deletions.
Basically, this means that your trigger runs on the background, and you specify when a process happens, based on different stages of when a record is processed before being added or removed from the database.
As long as a record is created/deleted from your force.com site, yes a trigger can be executed in the process.
If your tigger/apex code is failing for some reason, please include code snippets along with any error messages that we can use to help you. thanks!