Connection lines are useful for activating a function when an event happens. They can be used to activate a function when a part is touched, clicked, etc.

Here's the syntax for a connection line:

[Object].[Action]:connect([FunctionName])

Just for an example, a connection line for a simple onTouch script would look like this

Code:

script.Parent.Touched:connect(onTouch)

To find out what actions can be used with an object, go to the ROBLOX Wiki and search for the object you are looking for. It should come up with a table. Scroll to the bottom and look for the lighting bolts. Those are the actions of the brick. Example, "Part" has these actions:
AncestryChanged
Changed
ChildAdded
ChildRemoved
DescendantAdded
DescendantRemoving
LocalSimulationTouched
Touched

Nice Tutorial :D

Sometimes i see people do this:

Code:

[Object].[Action]:connect(function    [FunctionName(FunctionParameters]    end))

Why is this situation sometimes valid?

Instead of

Code:

function hi() print("Hi") end [Object].[Action]:connect(hi)

we can do

Code:

[Object].[Action]:connect(function() print("Hi") end end)

Its shorter and I like it more

Oh I see you just create a function out of thin air...

It can be useful. I can make a kill script that is only 3 lines with that.

I can make a lava script that is 2 lines:

Code:

script.Parent.Touched:connect(function(hit) hit:BreakJoints() wait(1) hit:Remove() end)

Short Player killer

Code:

script.Parent.Touched:connect(function(h) pcall(hit.Humanoid.Health = 0 end) end)

you forgot the function() at the start of the pcall. :o