It expresses an intention to perform an action for someone or something. For example:
* Haré por ti lo que pueda. (I will do for you what I can.)
* Haré por mejorar mi español. (I will do my best to improve my Spanish.)
Note: "Haré por" can also be translated as "I will try to" in some contexts.
Examples:
* Haré por estar ahí a tiempo. (I will try to be there on time.)
* Haré por ayudarte. (I will try to help you.)