when you create a new MS Teams you also creating a modern MS Group behind the scene stored in Azure AD. Additional a SharePoint site is created, teams are assigned a document library and channels are folders within this document library. you can add functionality to team with attaching apps and connectors as tabs to the a specific team.
Conversations are stored in the chat service leverages Azure storage and moving to Cosmos DB  . Chat and channel messages are also stored in Exchange. inline messages images and gif are stored in another Azure Micros Service Media store.
Files through Chat 1:1 or 1:N are uploaded to a personal OneDrive for Business and permission are set to the members of the chat. This is very important because if a member of the team is leaving and their One Drive is deleted all the files associated are no longer available to the team.
files that were uploaded to SharePoint are stored locally on the team site folder (by channel).
There are option to connect to 3th party storage services, for example, Dropbox, Box, Citrix ShareFile, Google Drive.
voicemail are stored using Azure voicemail Micro Service inside of the individuals exchange mailbox. Recording is done using Microsoft Stream which uses a Azure blob storage.
Scheduled meeting are placed inside individual mailbox for each member.
Azure Active Directory (AAD)
Multi Tenant, cloud based directory and identity management service, that allows Core Directory services and applications access management and identity protection. on-prem this was handled by Windows Active Directory on the cloud this is known as Azure Active Directory. You can have both on-prem and cloud AD using Microsoft Synchronization services.
AAD Free: included with an Azure subscription
AAD Basic ; used by task worked with cloud-first needs for example typical group based management tasks, self service password reset for cloud applications, and Azure AD application proxy which provide the organization to publish on premises web applications using AAD feature and functions.
AAD Premium P1 : adds enterprise-level identity management capabilities which provides Dynamic groups and self service group management.
AAD Premium P2 : adds identity protection and Privileged identity Management includes all P1 Features.
1- Azure Cosmos DB is Microsoft’s proprietary globally-distributed, multi-model database service "for managing data at planet-scale" launched in May 2017. It is schema-agnostic, horizontally scalable and generally classified as a NoSQL database.