Various categories of foreign-born persons who have the right to spend time in the U.S. do NOT have the right to work here as well, unless they have first applied for and received an employment authorization document (EAD), often referred to as a work permit. For example, asylees, people with a pending application for adjustment of status, fiance visa holders, spouses of E-1/E-2, J-1, and L-1 visa holders, and under some circumstances, students are among the non-citizens who may apply for a U.S. work permit.
In most cases, applicants must pay a fee for the work permit; though in some, such as adjustment of status cases, the fee is included in the overall green card application fee.
Even if you are not planning to work, having a work permit can be useful as a piece of photo identification. You can use it to get a Social Security card and a driver’s license.
If this is your first work permit, under “I am applying for,” check “Permission to accept employment.” If you’ve applied for a previous work permit (for example, if you’re applying now as part of your green card application but previously applied for and received a work permit as a fiancé), check the box for renewals.
Questions 1-14: Self-explanatory.
Questions 15 - 16: These can be difficult questions -- you will need to scan through the USCIS instructions to Form I-765 until you find your eligibility category. If, for example, you are applying for adjustment of status, you would page through the form until you see the are an “Adjustment Applicant,” and the Question 16:category "(c)(9)." Or, your category might be "F-1 Student Seeking Off-Campus Employment Due to Severe Economic Hardship," in which case you would enter those words in Question 15 and (c)(3)(iii) in Question 16.