I believe the terminology has changed from aloha apps to ISV apps.
Previously the main advantage was that installed ahola apps didn't count towards various org limits and could work with Group and Professional editions of Salesforce. In a previous Salesforce release at least some of the advantages were passed on to all managed packages.
Not much documentation appears to use the term "aloha" any more. There is an old blog post Design an Aloha App. The post linked to the Designing an Application for Group and Professional Edition page which now redirects to Architectural Considerations for Group and Professional Editions. I pulled the following out of the wiki history for the old page:
Furthermore, as part of the AppExchange Partner Program, your managed package will be eligible for special permissions allowing you to take advantage of unique benefits ensuring your app will properly install and function in GE and PE. Apps built on Force.com and which have these special permissions are called Aloha Apps. Aloha Apps will be featured on the AppExchange here.
Upon eligibility, an Aloha App is Apex authorized and immune to certain edition limits. In addition, if your app requires API integration, eligible partners can gain API access to GE and PE orgs. For more information on the Partner Program, including eligibility requirements, please visit us at www.salesforce.com/partners.
Note: Your app can only be an Aloha App and receive the Aloha App icon on your AppExchange listing if it's packaged as a managed package.
How to make an Aloha App?
By now, you understand there's many special permissions you can take advantage to build for GE and PE. If you've built an app and you think it's ready to work with GE/PE as is, you can log a case at the Partner Portal and create a case requesting any of the permissions mentioned (Apex Authorization, Apps/Objects/Tabs Limit Immunity, and/or API Access). Note that your application has to have a managed package associated with its listing and you must be an eligible partner. For more information on the Partner Program, including eligibility requirements, please visit us at www.salesforce.com/partners.
Keep in mind you may still need to re-architect your app to support GE/PE, even with these special permissions active. As a partner, you are entitled to various test environments to ensure your app will work properly against GE/PE, you can learn more here.
I think going forward you are better following the documentation from Using Apex in Group and Professional Editions
Once you've ensured that your app meets the requirements for Aloha status, you then need to raise a case in the partner portal asking for it to be granted, it's not automatic. There's a specific case category available for such requests.