Well, let's start:

1. No parameter, end!

The first issue you got was on calling function. You didn't set an parameter for giveSword function:

local replicatedstorage = game:GetService("ReplicatedStorage")
local weapons = replicatedstorage:WaitForChild("Weapons") 
local woodensword = weapons:WaitForChild("WoodenSword")
local knightssword = weapons:WaitForChild("KnightsSword")

function giveSword(player) -- you requested a player
    if player then -- if the player exists then do stuff
        local backpack = player:WaitForChild("Backpack")
        if backpack then
            local startergear = player:WaitForChild("StarterGear")
            if startergear then
                if player.Weapon.Value == "WoodenSword" then
                    woodensword:Clone().Parent = backpack
                    woodensword:Clone().Parent = startergear
                elseif player.Weapon.Value == "KnightsSword" then
                    knightssword:Clone().Parent = backpack
                    knightssword:Clone().Parent = startergear                   
                end
            end
        end
    end -- else do nothing
end

wait(5)
giveSword() -- you must to set who is the player, else, player will be set as nil, which means false on an if statement

So you need to set the player:

giveSword(game.Players:WaitForChild("Playername"))

2. Did you want to give sword for everyone, right?

To do that, you can use PlayerAdded event to apply that function to the new player:

local replicatedstorage = game:GetService("ReplicatedStorage")
local weapons = replicatedstorage:WaitForChild("Weapons") 
local woodensword = weapons:WaitForChild("WoodenSword")
local knightssword = weapons:WaitForChild("KnightsSword")

game.Players.PlayerAdded:connect(function(player) -- request the player from the event
local backpack = player:WaitForChild("Backpack")
        if backpack then
            local startergear = player:WaitForChild("StarterGear")
            if startergear then
                if player.Weapon.Value == "WoodenSword" then
                    woodensword:Clone().Parent = backpack
                    woodensword:Clone().Parent = startergear
                elseif player.Weapon.Value == "KnightsSword" then
                    knightssword:Clone().Parent = backpack
                    knightssword:Clone().Parent = startergear                   
                end
            end
        end
end)

But if you want to give sword to everyone at a certain time, we must to call a for loop:

local replicatedstorage = game:GetService("ReplicatedStorage")
local weapons = replicatedstorage:WaitForChild("Weapons") 
local woodensword = weapons:WaitForChild("WoodenSword")
local knightssword = weapons:WaitForChild("KnightsSword")

function giveSword()
for i, v in pairs(game.Players:GetChildren()) do
local backpack = v:WaitForChild("Backpack") -- v is the current player
        if backpack then
            local startergear = v:WaitForChild("StarterGear")
            if startergear then
                if v.Weapon.Value == "WoodenSword" then
                    woodensword:Clone().Parent = backpack
                    woodensword:Clone().Parent = startergear
                elseif v.Weapon.Value == "KnightsSword" then
                    knightssword:Clone().Parent = backpack
                    knightssword:Clone().Parent = startergear                   
                end
            end
        end
end
end

3. If statement for WaitForChild() ?

Statements requesting for a child provided by :WaitForChild() function are useless.

local replicatedstorage = game:GetService("ReplicatedStorage")
local weapons = replicatedstorage:WaitForChild("Weapons") 
local woodensword = weapons:WaitForChild("WoodenSword")
local knightssword = weapons:WaitForChild("KnightsSword")

game.Players.PlayerAdded:connect(function(player) -- request the player from the event
local backpack = player:WaitForChild("Backpack")
local startergear = player:WaitForChild("StarterGear")
local weaponval = player:WaitForChild("Weapon")
    if weaponval.Value == "WoodenSword" then
        woodensword:Clone().Parent = backpack
        woodensword:Clone().Parent = startergear
    end
    if weaponval.Value == "KnightsSword" then
        knightssword:Clone().Parent = backpack
        knightssword:Clone().Parent = startergear
    end
end)

4. Server or Client?

A thing you must to understand is that ReplicatedStorage is useful for LocalScripts, while if you use a Server Script, you should use ServerStorage instead.

Final Script

Once you want to give the swords a certain time, here it goes:

local weapons = game:GetService("ServerStorage"):WaitForChild("Weapons") 
local woodensword = weapons:WaitForChild("WoodenSword")
local knightssword = weapons:WaitForChild("KnightsSword")

function giveSword()
    for i, v in pairs(game.Players:GetChildren()) do
        local backpack = v:WaitForChild("Backpack") -- v is the current player
        local startergear = v:WaitForChild("StarterGear")
        if v.Weapon.Value == "WoodenSword" then
            woodensword:Clone().Parent = backpack
            woodensword:Clone().Parent = startergear
            elseif v.Weapon.Value == "KnightsSword" then
                knightssword:Clone().Parent = backpack
                knightssword:Clone().Parent = startergear                   
            end
        end
    end
    end
end

wait(5)
giveSword()