Weapon Level: determines what level your character needs to equip the weapon. In Fallout 76 weapon's level can scale depending on the enemies level you loot it from or your crafting skills. The level also determines the base damage of your weapon, and how big the condition bar is (the higher the level, the higher the chances of finding weapons with wider condition bar)
Condition: condition is a randomly generated attribute of every weapon, which determines how long it can be used without repairing it. Condition bar depends on the weapon level, your Intelligence attribute when crafting a weapon (players with high INT attribute can craft weapons with bigger condition bars) or Luck attribute when looting (the higher your Luck, the higher the chances of finding weapons in good condition)
Damage: your weapon's base damage, in general, is displayed per single Hit (each bullet, or one swing with your sword). Commonly misinterpreted stat, as in order to correctly estimate your firepower, you need to take into consideration the weapon's rate of fire (or attack speed) to calculate your DPS correctly
Rate of Fire: which indicates how many bullets are fired per minute (it's yet unclear if this also accurately applies to weapons in Fallout 76). The higher the Rate of Fire the more rounds are shot in the specified period of time. The vis-a-vis stat for Melee weapon is Attack Speed, which can be either slow, medium, fast, or very fast. Weapons with very high Rate of Fire or Attack Speed are great when combined with "Furious" Legendary Power, Concentrated Fire Perk, and "on Hit" effects like for example inflicting Radiation with attacks from Overly Generous Perk or chance to cripple limbs on hit.
Damage per Second (DPS): which is the product of Damage and your Rate of Fire (or Attack Speed). This is one of the most important stats of every weapon in Fallout 76, however, it's yet unclear how to properly calculate it
Accuracy Rating: determines your chance to hit in V.A.T.S., your chance to hit targets that are further away, and the sway speed and its range when aiming. Weapons Accuracy can be altered by modifications done to your weapon's Receiver, Barrel, Grip, and Scopes.
Range: effective range of the weapon. Your damage and Accuracy Rating will diminish if your target is further away. Modifying the Receiver and Barrel can increase (or decrease) your weapons range.
Other stats, that are rather self-explanatory include Ammo type, Magazine capacity, Weight, and Value.