While creating the web form, you might have enabled the Manual Approval of leads. In this case, the leads generated from the web form will be available under the Leads tab only if they are manually approved by the user with Administrator profile.

So, you need to check if the Manual Approval of leads is enabled for the web forms. To check, please do the following:

1. Click Setup > Lead Settings > Web-to-Lead form.
2. Select the web form, and then click Edit.
3. In the Web-to-Lead Form page, under the Lead Assignment section,  clear the checkbox. 
4. Click Save.
   For more details refer Approve Leads.