Now I was under the impression that the word 大きい was one word but their explanation seem to imply that the い is a suffix. Same thing with 美味しい。And if I understand correctly they are both I adjectives. Was this the case of them generalising their I-adjectives or??
Yep, the い in い-adjectives is suffix! It can’t stand on its own or be attached to words that aren’t い-adjectives, though.
In this case, です is just added for politeness. い-adjective + だ is ungrammatical.
ETA: The stem 大き (おおき) can be conjugated like this:
大きい → non-past
大きくない → non-past negation
大きかった → past
大きくなかった → past negation
大きく → adverb ‘in a big way’
大きさ - noun form ‘size’/bigness
(add です to any of these for extra politeness)
But also … it can be conjugated like this (so can 小さ, but most adjectives can’t):
大きな(noun)
implied (but unused): 大きだ・です - non-past
implied (but unused): 大きじゃない - non-past negation
implied (but unused): 大きだった・でした - past
implied (but unused): 大きじゃなかった・じゃなかったです - past negation
You’ll notice that ない is also an い-adjective, and so is the -たい form of verbs.