"轻快地走过" can be translated into English as "walked by briskly" or "strode by lightly".
Here are some example sentences to illustrate the usage:
1、 She walked by briskly, humming a tune under her breath.
她轻快地走过,嘴里哼着小曲。
2、 He strode by lightly, as if he had no worries in the world.
他轻快地走过,仿佛世上没有烦心事。