Simply put, LSM-Tree (Log-Structured Merge-Tree) is a leveled storage method. To achieve good read and write performance, it “caches” data and log records in a memory-resident tree (the $C_0$ tree), and regularly flushes the log records to the disk-resident trees (the $C_1$ tree). The disk-resident trees form a hierarchy ($C_1, C_2,$ etc.); when the trees of a lower level are full, some of them are merged into a higher level tree.
LevelDB stores disk-resident trees in SSTable (Sorted-String Table) files, which are fast to read, but slow to insert or delete. To offer fast insert and delete, LevelDB organizes these SSTable files into a LSM-Tree.