I noticed after I created a custom object, an object which ends with
__Tag has been created as well. What does this object mean?
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.