Totally means entirely, with nothing left out. Totally different, totally wrong, totally agree.
As an intensifier it is informal and has been overused to the point of weakening — totally now often means merely very. On its own as a reply it means yes emphatically, which is a Californian usage that spread worldwide. Note total, and that completely and utterly do the same work more formally.
1adverbtotallyEntirely, with nothing left out.
“I totally forgot about your birthday, and I'm so sorry!”
totally is an intensifier.
Also accepted in games: completely
Medieval Latin
tōtālis
Old French
total
Middle English
total
English
total
English, today
totally
From total + -ly. total comes from Middle English total, from Old French total, from Medieval Latin tōtālis, from tōtus + -ālis, the former element of unknown origin. Perhaps related to osc touto (“community, city-state”), xum 𐌕𐌏𐌕𐌀𐌌 (“tribe”), Old English þēod (“a nation, people, tribe”), from Proto-Indo-European tewtéh₂ (“people”). More at English Dutch, English thede.
Etymology from Wiktionary, CC BY-SA