CECHL01 is a model of PS3. in this case, the CECHL01 PS3 is a an 80 GB playstation model that was released in October of 2008. it has two USB ports, it is not backwards compatible, and it is no longer in production.
In November 2008 they released a 160 GB Fat PS3 CECHP01 that had the latest harddrive in the Fat models. Two 80 GB models (CECHK01 & CECHL01) were released in 2008 besides the 160 GB special edition
You might have one of the 2 models of PS3 80 GB that were released with 2 USB ports Models CECHK01 or CECHL01 released in August and October 2008 that do not play PS2 games. see related link
The PlayStation Move will work on any model PlayStation. The Move does require that the PS3 have current updates because certain software updates are needed to allow the move controller to work with the PS3. They had to in effect teach the PS3 that there was a new controller. These updates were needed for every PS3 and not just the model you asked about.