what is localhost:2559?

[leftisthominid]

I occasionally see benign blue spikes from this on my network shield

[DavidR]

We would need more information to give any real information other than very basic.

This is the very basic answer:
Localhost (IP address 127.0.0.1) as its name implies is your local system the : colon is essentially a separator and the number following that is the port number being used. However concerning yourself in 'benign' traffic isn't a good use of your time.

Additional information such as the process responsible for initiating this connection but you are unlikely to get that from the network shield traffic history. You would nee other tools to see what ports are in use and what processes/programs initiate them.

[leftisthominid]

So I presume, I should not be worrying about this?

[DavidR]

I wouldn't be unless there was something that happened to be interfering with the system, which I guess this isn't. But even then without detailed information no one can really say.