How can a monocot get so massive?
The vascular system is different in monocots and dicots. In dicots the vascular tissues are arranged in concentric circles; one of these rings is meristematic cells (undifferentiated cells that can differentiate into any cell type). This ring of meristem tissue is called the vascular cambium and is where secondary growth occurs - xylem grows inwards and phloem grows outwards.

Whereas:


  Monocots have a distinctive arrangement of vascular tissue known as an
  atactostele in which the vascular tissue is scattered rather than
  arranged in concentric rings. Many monocots are herbaceous and do not
  have the ability to increase the width of a stem (secondary growth)
  via the same kind of vascular cambium found in non-monocot woody
  plants. However, some monocots do have secondary growth, and because
  it does not arise from a single vascular cambium producing xylem
  inwards and phloem outwards, it is termed "anomalous secondary
  growth". (Wikipedia)


For palms specifically:


  Palm trees increase their trunk diameter due to division and
  enlargement of parenchyma cells, which is termed diffuse secondary
  growth. (Wikipedia)


Parenchyma cells are type of cells found in plant ground tissue, which makes up the bulk of plant mass.