When working with machinery in a manufacturing facility, Personal Protective Equipment (PPE) refers to protective clothing, hard hats, goggles, or other gear designed to protect the wearer's body from injury by workplace hazards (such as electrical and mechanical hazards). Examples of PPE include:

Eye protection -- Safety glasses, goggles, or face shields.

Head protection -- Hard Hats

Ear protection -- ear plugs

Foot protection -- steel-toe boots

Hand protection -- gloves

Arc Flash protection -- arc flash suits

Personal Protective Equipment provide one layer of protection against many of the hazards associated with industrial machines and equipment.

The actual PPE required varies for each and every factory. It is determined by the employer, based on their assessment of the hazards within the worksite. The requirement to determine the necessary PPE and to enforce the use of PPE falls entirely on the employers. As stated by OSHA:

OSHA Title 29 CFR 1910.132(d)(1)
The employer shall assess the workplace to determine if hazards are present, or are likely to be present, which necessitate the use of personal protective equipment (PPE). If such hazards are present, or likely to be present, the employer shall:
i)        Select, and have each affected employee use, the types of PPE that will protect the affected employee from the hazards identified in the hazard assessment;
ii)        Communicate selection decisions to each affected employee; and,
iii)         Select PPE that properly fits each affected employee.

OSHA Title 29 CFR 1910.132(d)(2)
The employer shall verify that the required workplace hazard assessment has been performed through a written certification that identifies the workplace evaluated; the person certifying that the evaluation has been performed; the date(s) of the hazard assessment; and, which identifies the document as a certification of hazard assessment.

For many types of PPE (e.g. eye protection, ear protection), OSHA further refines their rules specifically for that type of protection. For example, according to OSHA, the requirement for Eye and Face Protection is as follows:

OSHA Title 29 CFR Part 1910.133 Eye and Face Protection
The employer shall ensure that each affected employee uses appropriate eye or face protection when exposed to eye or face hazards from flying particles, molten metal, liquid chemicals, acids or caustic liquids, chemical gases or vapors, or potentially injurious light radiation.

Further Resources
OSHA's regulations on PPE can be found in Title 29, Code of Federal Regulations 1910 Subpart I -- See the OSHA page for a direct link.
The ANSI standard that covers general PPE is ANSI/NFPA 70E -- Personal Protective Equipment.