I want to ask a question about salesforce security. I have developed a real estate application on salesforce. Only those users can access my application who are created in my org. But If we install our app in another org's installed packages. Then it's asking for my org's credentials or any of my org's user's credentials. Kindly help me.
The package itself should not contain any information on users or their credentials. That is stored in the org.
If the real estate app data is stored as Salesforce data (ie: objects, etc), when you install the package on another org, only the metadata (not the data) is copied onto the new org. Any real estate data created in the new org will not be visible in 'your' org and vice versa. Likewise, the user database is independent from the original org.
That is, unless your app is getting the data by doing callouts to an external web service to get the data from another database.
As @martin said above, you need to be more specific as to how your app works and what issue you see if you want more help.