Adjectives have declension based on case. Hund takes the nominative case here, so "langsam" becomes "langsamer", with the -er coming from male singular nominative declension.
There is a good table on adjective declension here: https://www.duolingo.com/skill/de/Colors/tips-and-notes
Possessive pronouns trigger the same declension as the indefinite article (a/an), so "langsamer" means "slow" here.
This exercise is meant to show how the ending added by male singular nominative declension produces the same word as the comparative ending. For example:
Mein langsamer Hund schläft. - My slow dog sleeps.
Mein Hund ist langsamer als eine Katze - My dog is slower than a cat.
Mein langsamerer Hund ist braun. - My slower dog is brown
In the first two examples, "langsamer" has two different meanings, while in the third there are both the declension and the comparative ending, producing what looks like a double declension.