Improvised Weapons
Improvised weapons are not weapons that you are trained to use. They are simply things that are around when you need them in a fight. Improvised weapons include things like rocks on the ground, punching and kicking. When you use an improvised weapon you are typically interacting with the environment around you. Improvised weapons do not provide much of a bonus even if you are proficient in using them.
Simple Weapons
Simple weapons are those that require minimal training or no training at all. They are weapons that any character or class of character can use with some degree of skill or after a small amount of training. Simple weapons include slings, spears, crossbows and a staff. Different classes and races of characters tend to favor certain types of weapons and will start with certain proficiencies. Proficiency in simple weapons means that you will be more effective when you try to use this weapon.
Military Weapons
Military weapons are also known as martial weapons. These are the weapons that a fighter uses and you need to be trained in order to use these weapons effectively. Characters that use military weapons well include fighters, barbarians and paladins. These are the characters that typically attain proficiency with military weapons. Spellcasters and rogues tend to favor simple weapons and are not usually proficient in military weapons. Typical military weapons include axes, flails, swords, hammers, clubs and bows.
Superior Weapons
Superior weapons are specialized weapons that perform better than most military weapons but require specialized training. These usually require a weapon proficiency feat. Superior weapons include bastard sword, whip, dwarven axe, two-bladed swords, hand crossbows, repeating crossbows and katanas. Generally only warrior style classes use superior weapons since it takes some effort to become proficient with them. Most characters who specialize in a superior weapon prefer to use that weapon over all others.