Teams were clearly introduced to compete with Slack. Though, why did slack become popular? So perhaps check out this to see what MS was trying to copy.
Some teams will certainly like Teams, while other teams will prefer the more traditional route of Groups or Yammer. Though, creating a Team will create a Group, so teams really aren’t choosing between a Team and a Group, but rather it’s choosing to use either a Group or a Group plus a Team. Likewise, creating a Site will now create a Group. In the past, a Group had a Site, but again, now all new Sites will have Groups (to be precise, new Site Collections). So, create a Site, which also gives you a Group. Then, optionally, create a Team based on the Group, which is, of course, connected to the Site. Again, see the above article for the advantages of Teams, but it really comes down to preference. Some teams prefer to use email for team conversations, and so those teams should use Groups. Other teams prefer for all intra-team communication to be hosted in an app and to avoid email, and so those teams should use Teams.
Planner is available for teams who need task management. Of course, tasks could be assigned via email, but many teams prefer having better tracking capabilities and such, and so those teams should use Planner. Plans are associated with Groups, so organizations that want to use Planner will need to be using Groups. As mentioned above, when a Team is created, a Group is also created, so Teams can use planner due to the fact that their Team is already connected to a Group.
Yammer is the odd one out. It’s not replaced by Teams or Groups, as Teams can have a max of 600 members on a Team, and Microsoft suggests keeping Groups to below 1000 members for performance reasons. Yammer is not replaced by a single Group, as Yammer supports multiple, threaded conversations across multiple groups. Perhaps Yammer is a preference vs O365 Groups in smaller organizations? Except, that they just announced that Yammer will be able to integrate with Groups, giving Yammer the ability to utilize Group resources, such as the Group document library, OneNote, and Planner. So perhaps Yammer is positioned as the Enterprise Social Network, while Groups are better suited for small/medium company or departmental level efforts? Again, personal preference may come in here as well.