Why is only the first part of my script is running?

You're trying to do 2 while loops in the same script. This will not work as they are running in the same thread.

You don't even need 2 while loops, you just need 1 loop and an if then elseif end statement.

Use Coroutine's to fix this, run each while loop in a different thread!

local cow = script.Parent
local animation = cow.Animation
local humanoid = cow.Humanoid
local track = humanoid:LoadAnimation(animation)

local animFunction = coroutine.wrap(function()
    while wait(1) do
        if cow.HumanoidRootPart.Velocity.Magnitude >= 6 then
            track:Play()
            print("Playing")
        elseif cow.HumanoidRootPart.Velocity.Magnitude <= 5 then
            track:Stop()
            print("Stopped")
        end
    end
end)

animFunction()

Hope this helped! Feel free to select this as an answer if this helped you!

The first while loop is preventing the second one to run. Since the first loop never ends, the second loop never has a chance to start. In your case, this could simply be solved by merging the two.

local animation = script.Parent.Animation
local humanoid = script.Parent.Humanoid
local animationTrack = humanoid:LoadAnimation(animation)
local cow = script.Parent

while true do
    wait(1)
    if script.Parent.HumanoidRootPart.Velocity.Magnitude >= 6 then
        animationTrack:Play()
        print("playing")
    elseif script.Parent.HumanoidRootPart.Velocity.Magnitude <= 5 then
        animationTrack:Stop()
        print("Stopped")
    end
end 

In other cases where you really need to have both loops running simultaneously, you'd use coroutines. Generally though, the fewer threads, the faster the performance