A blech is a metal sheet used by many observant Jews to cover stovetop burners (and for some, the knobs/dials too) on Shabbat

Shabbat

Shabbat is the seventh day of the Jewish week and a day of rest in Judaism. Shabbat is observed from a few minutes before sunset on Friday evening until a few minutes after when one would expect to be able to see three stars in the sky on Saturday night. The exact times, therefore, differ from...

 (the Jewish Sabbath), as part of the precautions taken to avoid violating the halachic

Halakha

Halakha — also transliterated Halocho , or Halacha — is the collective body of Jewish law, including biblical law and later talmudic and rabbinic law, as well as customs and traditions.Judaism classically draws no distinction in its laws between religious and ostensibly non-religious life; Jewish...

 prohibition against cooking on the Sabbath.

Common use

(Following excerpt with permission of publisher of The Blech Book—The Complete & Illustrated Guide To Shabbos Hotplates, by Rabbi Fishel Jacobs.)

• The food (including water) intended for Shabbat use, should be completely cooked.
• The stove’s gas flames or electric coils are turned on. The blech is placed over these. Alternatively, the Shabbat hot plate
  Hot plate
  A hot plate is a portable self-contained tabletop small appliance that features one, two or more gas burners or electric heating elements. A hot plate can be used as a stand alone appliance, but is often used as a substitute for one of the burners from an oven range or the cook top of a stove...
  
  , which needs no blech (when it is the type which has no knobs to adjust the heat level,) is plugged in.
• The pot is placed on the blech. Note: It is permissible to place another pot on this one.
• The pot on the blech, or another pot which has been placed on it, may be covered with a blanket, clothing, towel, cloth etc. to keep the heat from dissipating. One side of the pot should be left partially uncovered.

During Shabbos, the pots are removed according to need. After removal, it is permissible to return the pot onto the blech, following these guidelines:

• The pot should be removed from the blech with the intention to replace it afterwards and held at all times, not leaned onto any surface. (A heavy or unwieldy pot may be partially leaned on a surface, while being held, if there is no alternative.)
• The food must be in the same pot, completely cooked, and has retained at least some of its original heat.

The permissibility of blech (and unblech, below) and the acceptable manner of their use is questioned by several modern kashrut

Kashrut

Kashrut is the set of Jewish dietary laws. Food in accord with halakha is termed kosher in English, from the Ashkenazi pronunciation of the Hebrew term kashér , meaning "fit" Kashrut (also kashruth or kashrus) is the set of Jewish dietary laws. Food in accord with halakha (Jewish law) is termed...

organizations; however, the use of a blech to reheat food on the Sabbath remains very popular among observant Jews.

Unblech

An unblech, or K'Deira Blech (lit. "pot blech", commonly referred to as "water blech"), is also used to heat up pre-cooked food on the Sabbath, but utilizes different halakhic mechanisms from a standard blech. An unblech consists of a shallow metal pan filled with hot water and covered by another metal pan, and thus is akin to a pot of warm food for halakhic purposes. As such, it may be more flexible than a standard blech for halakhic purposes. However, the temperature of an unblech is limited by the boiling point of water and is not as hot as a typical blech.