The WEP key is the encryption key your wireless router uses to stop unauthorised people accessing the network. When you set yours up, you'll have set the key so your computer or laptop can access your network. All you need to do is use that same key on the DSi to access the network.
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It's usually a WEP Key issue.
it is a type of a code or password to get on the internet
The WEP key is part of your router and it would be the same thing your PC or laptops use to connect to your wireless network. On Windows 7 you can left click on your connection icon, right click on your connection and select properties, then on the security tab there's the option to show your WEP key. Or, you could check your router's documentation, as you can log into the router's control panel through a PC browser, you can see the WEP key there. Lastly, sometimes the WEP key is on a label on the router itself, as part of its default settings, check that also.
eg wrong password or you are not close enough to your internet access point and check WEP instead of WPA
A WEP key has nothing to do with your DS system but the WEP key is the password that is needed for secured wireless modem networks when you're trying to set up the connection with other devices. Most default WEP keys can be on the router or the modem already but if the key isn't a default one then you'll have to ask whoever set up your modem or Router for the WEP key.