A Mashgiach (Hebrew: משגיח, pl. משגיחים, mashgichim, lit. "Supervisor") is a Jew who supervises the kashrut status of a kosher establishment. A mashgiah may supervise any type of food service establishment, including slaughterhouses, food manufacturers, hotels, caterers, nursing homes, restaurants, butchers, groceries, or cooperatives. The mashgiach usually works as the on-site supervisor and inspector, representing the kashrut organization or a local rabbi, who actually makes the policy decisions for what is or is not acceptably kosher. Sometimes the certifying rabbi (Hebrew: רב המכשיר, rav hamachshir) acts as his own mashgiach; such is the case in many small communities.
The usual requirements for becoming a mashgiach are being Jewish, observing the sabbath (shomer Shabbat), observing the laws of kashrut (shomer kashrut), and doing mitzvot, the commandments of the Torah (shomer mitzvot). Different rabbis will have different requirements. Even the same rabbi may have different requirements, depending on the type of establishment being supervised (for example, supervision of a slaughterhouse will be very different from supervision of a grocery). Sometimes the only requirement is that the person is Jewish and knowledgeable of the laws of kashrut. The observant Jew can be a man or a woman. 
Regardless of specific eligibility requirements for a mashgiach, they take on a great responsibility and the burden of a community. The mashgiach puts their good name and the name of the community on everything done on their watch.
A mashgiach is required whenever meat or fish is prepared or cooked. They check fresh eggs for blood spots before they are used in cooking, and must inspect all vegetables for forbidden insects before use.
The mashgiach is responsible for performing the The Mitzvah of Challah, the tithe of dough set aside for consumption by a Kohen (some perform this in the diaspora whereas in Israel it is always burnt).
The mashgiach must also light pilot lights and turn on cooking and heating equipment to satisfy minimum requirements of Bishul Yisroel (food cooked by a Jew) and Pas Yisroel (bread baked by a Jew), in a way that a Jew must be involved in the cooking of any kosher food "fit for a king's table."  To satisfy requirements for Sephardic Jews, the mashgiah may be required to play an even more active role in the cooking process.
One of the most pressing and often difficult jobs of a mashgiach, however, is the checking in and verification of shipments. The mashgiach must ensure that every food product that arrives at the facility has a reliable hekhsher before it is used. Suppliers often substitute products that are out of stock with non-kosher products. Non-kosher establishments would generally not mind these substitutions. For a kosher establishment, however, these substitutions can cause major problems. If a product arrives without a hekhsher, the mashgiach must make sure the product is clearly marked as non-kosher and is not used, but returned to the supplier. Sometimes a product arrives that is purportedly kosher, but no hekhsher can be found. In this case, the mashgiach obtains a valid letter of certification from the certifying rabbi or kashrut agency, usually by contacting the manufacturer. In addition to checking hekhsherim, the mashgiach must also check that all meat products that arrive are double sealed, usually by inner and outer plastic bags or an inner plastic bag and a sealed box, and that all wine is kosher wine.
Great strides, in the last several years, have been made towards ensuring that kosher products are transported only in kosher approved tanker trucks. 
(In many settings the mashgiach is merely responsible for making sure that the above tasks are performed by responsible, knowledgeable, and well-trained persons.)
A mashgiach plays social as well as technical roles in explaining kosher rules to the Jewish and non-Jewish community and forging close relationships with employees and customers. 
- Kosher foods
- Kosher wine
- Hekhsher (also "hechsher" or "hechscher")
- Traif (also "tref", "treif", or "treyf")
- Schochet / Schlachtmann