As much as one can; as far as possible. Similar to 'できるだけ' or 'なるべく'.
できる限り早く来てください。
Please come as soon as possible.
プロジェクトのためにできる限り協力します。
I'll cooperate as much as possible for the project.
できる限り多くの情報を集めて報告してください。
Please gather as much information as possible and report it.
健康のために、できる限り毎日歩くようにしている。
For my health, I try to walk every day as much as possible.