What does this mean in the output?

01:30:11.864 - Workspace.Model.Button.Regen:20: attempt to index field 'Parent' (a nil value)

I'm guessing it means i'm missing a value, but what does ":20" refer to? Line 20?

It follows the format

Time - ScriptTriggeringError:LineNumber: message

attempt to index (a value)

Means that you are trying index on A -- that is, use either A.something, A:something or A[something]. An attempt was made (but it can't, hence an error).

A field means a property. That is, you're indexing on something.Parent (e.g., something.Parent.Parent would cause this error)

(a nil value)

clarifies that the reason you can't index on something.Parent is that something.Parent is nil (which means either something is an object without Parent defined (some Lua table) or a ROBLOX object that hasn't been parented / has been Destroyed or Removed)