It's security for your wireless. No it's not essential, but I would suggest it you don't want others to be able to connect to your open wireless network!
In terms of the Wii. It doesn't matter either way.
Its very easy. I believe you go to Wii Settings -> Settings -> Internet to setup your connection. It prompts you to choose your security, you choose WEP and
it asks you for your Key. It then tests and all that jazz.