Mercado Central (translated as 'Central Market'), located on the edge of downtown Santiago and across from the Mapocho river, was at one time Santiago's central marketplace. Originally it was the Mercado de Abastos and was located in Plaza de Armas up until 1817. It was then moved by Chile's liberator, Bernardo O’Higgins, to the site it is today although the current building wasn't constructed until later that century, in 1864.
Today, it is still home to the fish market but anything beyond that and you'll be much better off crossing the river to Santiago's 'real' central market, La Vega Central. You can still buy fruits and vegetables here but it's all overpriced and mostly here for the sake of the tourist.
What the market is good for is authentic Chilean dishes especially where seafood is used. The main part of the building is made up of many restaurants on the outer edge with seating in the center. Entering it though is more like going into a used car lot with each restaurant pushing the hard sell (in English of course) to get you to sit with them and not their next competitor. If you can get by this otherwise annoying experience, you may be able to enjoy some truly satisfying Chilean cuisine.
To get there, you can take the Metro line 2 to station Puente Cal y Canto. If you are walking in the downtown area, it's just a couple of minutes from Plaza de Armas. There are two paseos (pedestrian streets) that both start from the main street and lead to the plaza. One of these is Paseo Ahumada. Once it crosses the plaza, it's name changes to Paseo Puente. Just walk down Puente a couple of blocks until you see the river and Mercado Central will be on your right.