History progresses as old ideas give way to new ones.
Literal
History [topic-は], old thoughts [subject-が] new thoughts [to-に] way [object-を] giving, progresses.
道を譲る ('to give way, yield the road') is a set phrase meaning to let someone or something pass or take precedence. The て-form 譲りながら combines with ながら ('while') — 'while yielding.' 進行する ('to progress, advance') is formal Sino-Japanese.