When creating a team, there is an optional field called "Company/Group Affiliation".  This ia text field that gives you some idea about the group creating the team:

In Salesforce, when the team record is created, this 'Company/Group Affiliation' populates the field "Organization Text".  

Then, if you wish to associate the team with an existing organization record, you can manually edit the lookup field "Organization" and actually associate the team with an existing organization, if you desire.

1) A new field "Type of Group" is added to the team creation process.   This allows you to get more information about what sort of group the team is:

The picklist options can be added to or edited (except for "Family & Friends", which has a special function with this feature.

2. The field "Company / Group Affiliation now becomes a 'smart search'.   You administratively decide which accounts/organizations in your Salesforce information you want to appear as options, and when the team captain types in the company/group name -- it will look for matches from your Salesforce data, and allow any existing organizations (that you've specified to show up in search), to be selected.  

If an existing match is found and selected:

The Team Record will automatically populate the lookup field and associate the team with the organization record.

If an existing match is not found:

If someone types in a company or group name that isn't in your Salesforce data as an existing account you've enabled for team lookup - then a message will be displayed:

Clicking on "Click here to enter a new organization" will put whatever Company / Group Affiliation they've entered into the team record in the field "Organization (Text)" as it did previously.   (It will not create a new account in Salesforce -- but you can choose to do that if you desire -- or just except the affiliation name text as a reference to the team.

If the type of group is specified as "Family & Friends" - then the "Search and Select your organization option" will not be displayed.  This is because you are not going to have organization records for families and teams made up of friends.

By not displaying the "Search and Select" dialog, it saves them a step and possible confusion :-)

See this article for information on requesting this feature, and the administrative steps you need to do to begin using it.