Mastodon is a federated social network - unlike Twitter or Facebook say, which is run by one company, it's easiest to think of Mastodon as a tool like email. There are a number of different servers or "instances" where your data (your account details, the contents of your posts, the timestamps of your activity, the cute picture you took of your cat fighting your slippers) are stored, there are a number of different apps or clients you can use to access these data the same way you could access the same email account through Apple mail on your iPhone or Outlook on your work PC or Gmail on an Android phone, and Mastodon is the set of instructions that allows them all to talk to one another.