To replicate:

1. Create a "Visible to:" multi-user picker custom field
2. Create an issue-level security scheme
3. Create a security level, and add the "Visible to" custom field as a member to that level
4. Set a project to use the security scheme and level
5. Create an issue, and add your own username to the "Visible to" field

The issue will be visible to you (and no-one else) when accessed directly. However when searching, this issue will not show up for you.