Magical implements work like weapons as far as equipping them and then attacking with them, but they are unaffected by distance and use you and your target's respective magical abilities rather than the normal attack and defense scores. This makes them very reliable in the hands of a wizard, except when fighting another wizard... not a bad idea to have a physical weapon as a back-up for those cases, if you're traveling solo.
Implements also give a bonus to actual spellcasting (they don't boost your magic for attacks). The basic implements in order of power are the sigil, orb, wand, and staff. The versions available for sell in the starting town have no effects beyond the casting bonus and the ability to attack with magic, but ones found thereafter are more than commonly likely to carry additional magical effects.
The purpose of implements is to create single-target at-will attack spells that are independent of the normal spell system, which is dependent on expendable scrolls that cost money, are mostly intended to be cast at the outset of a battle, and never require active targeting. Since this game has multiclassing baked in, if there wasn't a way for wizards to fight as wizards from "round to round" in combat, there would never be reason to be a full-on wizard. As things stand, a warrior/wizard is one of the best solo combat builds. The use of spells to soften up enemies (or buff up oneself) makes melee combat markedly easier, though the additional expense means you'll gain money for better gear more slowly.
Some pictures of the orb can be seen below.
Bowling for bandits.
You're a kitty!
The telltale hearts in the first pic signify that something has just taken damage. In this case, I happened to snap the screenshot right after the bandit defeated my cat.
The cat is a natural choice for a wizard's companion because they do give a boost to your magic whenever they're around. This doesn't mean they're the only option... a badger or bear will be better at keeping enemies off of you.