Implements are the four gear slots on every character: Head, Neck, Secondary Weapon and Accessory. The Secondary Weapon is a stat piece, not a second weapon, and has nothing to do with the Motive. Head and Neck pieces open with DEF and HP, Secondary Weapon and Accessory pieces with ATK and DEF, and every piece adds three more fixed lines.
Nothing rolls and nothing levels up. Two copies of the same piece at the same rarity and level are identical, as Vyncent Remethar and Rexlent both showed on camera, and a piece stays at the level it dropped at. Pieces drop at Lv. 20, 40, 60, 70 or 80; the beta footage reached 60, and fan-compiled data says your character's level must match or exceed the piece's to equip it. That makes a best-in-slot set a fixed target: keep one set per character and clear out the rest.
Rarity runs gray, green, blue, purple and orange, and it only scales the numbers. How much depends on the level. On Defender of Justice, the HP line reads 381, 383, 386, 391, 558 at Lv. 20 from gray to orange, nearly flat until orange, and 487, 682, 955, 1,364, 1,949 at Lv. 60, where purple is exactly twice green. Orange is in the files but could not be obtained in the beta. The files round percentages to one decimal and the game shows two, so a 3.1% here reads 3.09% on screen.