I noticed after I created a custom object, an object which ends with
__Tag has been created as well. What does this object mean?
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These objects (tables) are automatically created when tags are enabled in an org and provide the storage mechanism for those tags.
Tags are ad-hoc labels that can be applied to records; they are a way of grouping data.
A good overview article on tags is Salesforce Tags – The Good, The Bad, Limitations, and The Future. This article suggests that Chatter hashtags may eventually replace these tags.
PS "Eventually" has happened - see ca_peterson's comment.