The process by which your bones lengthen (during childhood and adolescence) is known as longitudinal bone growth.  It’s more complicated than you might think, so I’ve simplified it here.  There’s a strip of cartilage (the epiphyseal plate, or growth plate) embedded in each end of the bone, and that’s where all the lengthening growth occurs.

Within that plate, a remarkable process occurs.  First, as you might expect, the cartilage cells grow and divide, and this is what actually lengthens the bone.  But next, the cartilage cells essentially commit mass suicide, by creating a chemical “prison” that blocks the entry of nutrients and oxygen.  As the tissue dies it leaves a space behind, where bone cells can come in and add hard bone matrix.  Ultimately, this means the bone lengthens, and the whole “construction team” of cells follows the growth region as it extends further out.  It’s analogous to a road construction crew, where you have workers engaged in all steps of construction, but positioned at different points along the road.

But instead of painting a “center line,” the final step for our bone construction team is to lengthen the internal space of the bone.  This is known as the medullary cavity, and it’s there to make the bone lighter, and to house other important tissues (like bone marrow).  A group of “demolition” cells called osteoclasts lives near the end of the medullary cavity and continually eats away at the bone matrix.  This lengthens the medullary cavity, keeping its size in correct proportion, as the bone grows longer.

Why start with cartilage at all?  Unlike bone, cartilage is mostly water so it’s an easy tissue to rapidly assemble during early development.  Later in development, most of this cartilage is replaced by bone, but an important remnant of that early cartilage is the growth plate discussed here, which persists until adult height is reached.