。
She ran as fast as she could.
Literal
She [topic-は] [as much as possible-できる限り] fast ran.
できる限り is the slightly more formal of the two near-synonymous 'as much as possible' frames; the everyday counterpart is できるだけ. Both attach as adverbials before a verb or modifying clause, and both work for any 'maxing out' sense — speed, time, money, effort. 速く is the い-adjective adverbial of 速い ('fast'), formed by replacing い with く. Note 速い (fast in motion) versus 早い (early in time) — same reading, very different meaning, distinguished only by kanji.