Onward means continuing forward from here. Not stopping at this point — carrying on past it.
Travel uses it precisely, and an onward flight or onward journey is the next leg after this one, which is why border officials ask for proof of onward travel. In time it means from then on, as in from 1945 onward. British English usually adds an s for the adverb, giving onwards, and keeps onward for the adjective. There is also the rousing sense of pressing on, as in onward and upward.
Proto-Indo-European
*wer- — to heed, defend
Proto-Germanic
*warduz — guard, keeper
Old English
weard — keeper, watchman, guard, guardian, protector; lord, king; possessor
Middle English
warde
English
ward
English, today
onward
From on + -ward. ward comes from Middle English warde, from Old English weard (“keeper, watchman, guard, guardian, protector; lord, king; possessor”), from Proto-Germanic warduz (“guard, keeper”), from Proto-Indo-European wer- (“to heed, defend”). Cognate with Dutch waard, German Wart.
Etymology from Wiktionary, CC BY-SA