Freely means without restriction, or without being forced. Move freely, freely available, freely admitted.
Freely admitted is the interesting use — it means the person volunteered something against their own interest, which is why it carries weight. Freely available means no barrier rather than no cost. Note free, whose Old English sense was noble as well as unbound.
1adverbfreelyWithout restriction or force.
“Birds fly freely between the trees in the huge aviary.”
freely is a manner.
Old English freolice is free plus the -lice ending. Free once meant noble or beloved as well as unbound.
Old English
frēolīc — free, freeborn, glorious, stately, magnificent, noble, beautiful, charming
Middle English
frely
English, today
freely
From Middle English frely, freelich, from Old English frēolīc (“free, freeborn, glorious, stately, magnificent, noble, beautiful, charming”), equivalent to free + ly. Compare Middle Low German vrilik, vrigelik (“free”), Middle High German vrīlich (“free”).
Etymology from Wiktionary, CC BY-SA