For the sake of, in order to
This pattern is used when performing an action for the sake of something or to accomplish something. Specifically, it indicates the speaker will do what is stated in the second clause for the sake of what is stated in the first clause.
In the case of a noun being the reason for the action, 을/를 위해서 is used. 위해서 is the shortened form of 위하여서. Further, 서 can also be omitted, leaving 위해. It corresponds to 'for the sake of' or '(in order) to' in English. When used with a verb, -기 위해서 is added to the verb stem.
-기 위해서 cannot be added directly to adjectives. However, if -아/어지다 has been added to an adjective, making it a verb, then it can be used with -기 위해서.
Comparison:
Used when doing something to achieve a goal or for a specific purpose.
Can also be used with verbs in the form of 기 위해(서)
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