Some monocots (such as palms) are impressively thick and massive, yet botanists maintain that they don't have secondary growth. Why do botanists say this? How can it get so big without secondary growth?
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.
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.