An expression meaning as soon as possible / as quickly as possible — i.e., as fast as one can; commonly used in requests and instructions.
できるだけ早くご回答ください。
Please reply as soon as possible.
この問題はできるだけ早く解決する必要がある。
This issue needs to be resolved as quickly as possible.
できるだけ早く病院へ連れて行ってください。
Please take (them) to the hospital as soon as possible.