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Singled homed means the NOC has one bandwidth provider, usually Cogent. This is normally the more economical of the 2 choices.
The downside to this is if that provider goes down, so does your website.
BGP4 Redundant refers to Border Gateway Protocol. BGP selects the quickest route to the destination and sends the information along that route. Also, if one network provider goes down the NOC has several more carriers to take over so your website (shouldn't) go down.
Not too technical, but maybe it helps you get the idea.