From Bulbapedia, the community-driven Pokémon encyclopedia.
Movement speed is a mechanic of the Pokémon Mystery Dungeon series, and is the series' analogue of the Speed stat. It primarily governs the number of actions (such as moving, attacking, or using an item) a Pokémon may take in a given turn.
Normally, Pokémon may take only one action in a given turn; however, Pokémon may have their movement speeds boosted or dropped. Each Pokémon may have up to five simultaneous boosts in movement speed and five simultaneous drops in movement speed, not counting permanent boosts such as from snowy weather (for Ice-type Pokémon), the Ability Speed Boost, the Time Tripper IQ skill, or Deoxys Speed Forme's boost. Similarly, as long as a Pokémon is Paralyzed, it suffers from a permanent speed drop, which does not count against the five. Each boost in movement speed negates a drop in movement speed. A Pokémon may take one additional action per turn for each boost in movement speed that is not negated, up to a maximum of four actions per turn. Conversely, a Pokémon can only take one action every two turns if there is a drop in movement speed that is not negated.
Boosts in movement speed last anywhere between 8-10 turns, while drops in movement speed last anywhere between 6-8 turns. A drop in movement speed is considered a status ailment and not a stat reduction (as there is no speed stat in Mystery Dungeon), and thus can be healed by changing floors and exiting the dungeon. Any change in movement speed will be removed by stepping on a Wonder Tile. It also means that moves that prevent stat drops or clear them (such as Haze) do not affect movement speed.