Enthusiastically means with keen and eager interest. Whatever it is, you want to be doing it.
It attaches to verbs of agreement and of action, so agreeing enthusiastically, nodding enthusiastically and enthusiastically taking something up are all standard. There is a common ironic use, since describing somebody as enthusiastically unqualified is a joke that works precisely because the adverb is so positive. The adjective enthusiastic and the noun enthusiasm belong with it, and an enthusiast is somebody devoted to a pursuit.
1adverbenthusiasticallyWith eager interest and enjoyment.
“They enthusiastically agreed to the whole plan.”
Proto-Indo-European
*leyǵ- — to bind, tie
Latin
alligāre
Old French
alier — to join together, unite; to alloy (metals); (cooking) to combine ingredients
Middle French
alier
Anglo-Norman
alier
Middle English
allien
English
ally
English, today
enthusiastically
Built from
From enthusiastic + -ally. ally comes from Middle English allien, alien (“to form an alliance, associate, join; to become an ally; to introduce (someone) as an ally; to marry; to become related (to someone); to attack, engage in combat; to combine; (cooking) to combine ingredients, especially to bind them together”)alie, alleye, allie, ally, allye, aly, alye, alyȝe, from Anglo-Norman alier, allier, Middle French alier, allierallyer, alyer, and Old French alier (“to join together, unite; to alloy (metals); (cooking) to combine ingredients”) (modern French allier), from Latin alligāre, the present active infinitive of alligō, adligō (“to bind around, to, or up (something), bandage, fasten, fetter, tie; to hold fast; to detain, hinder”), from al-, ad- + ligō (“to bind, tie; to bandage, wrap around; to unite”) (from Proto-Indo-European leyǵ- (“to bind, tie”)). a doublet of allay and alligate and alloy and ligament.
Etymology from Wiktionary, CC BY-SA