This structure is called the Palace and was probably the ceremonial and administrative center of the city of Palenque in the 7th and 8th centuries CE.
The Palace is a rather dense assembly of corridors, courtyards, and subterranean passageways.
Although sumptuously decorated with painted stucco figures, it probably was not the royal residence, but rather more the political and ritual center of Palenque, where the royal court of the ruler could show off power, wealth, and influence.
Photograph of Palenque taken by A.P. Maudslay (1881/1894) by Alfred Percival MaudslayBritish Museum
When Maudslay spent months in Palenque in 1891, he lived in a still-intact chamber in the Palace and employed many men to not only cut the jungle, but also to excavate part of the structures and clear the monuments.
Photograph of Palenque taken by A.P. Maudslay (1881/1894) by Alfred Percival MaudslayBritish Museum
In this photo from 1891 you can see the amount of debris that Maudslay cleared from this part of the Palace, including many stones from the fallen facade.
You can also see some of the stucco ornaments on the pillars and wall at the back.
Photograph of Palenque taken by A.P. Maudslay (1881/1894) by Alfred Percival MaudslayBritish Museum
This is House C in one of the courtyards of the Palace – the place where Maudslay had his explorer's quarters in 1891.
You see his bed, 'wardrobe', and some equipment in the background inside the building.