Microtubules are hollow cytoskeletal polymers built from repeating $\alpha$-tubulin/$\beta$-tubulin dimers. Because every dimer is oriented the same way in the polymer, a microtubule is polar: its two ends are structurally different and are called the plus end and minus end.

This polarity matters because the two ends usually have different growth behavior and because motor proteins can move directionally along the microtubule lattice.

Growth and shrinkage are dynamic

Tubulin dimers bind the nucleotide GTP. A tubulin dimer can be added to a growing microtubule, and GTP associated with incorporated tubulin is later hydrolyzed.

A growing end that retains a stabilizing region of recently added GTP-bound tubulin is relatively resistant to disassembly. If that stabilizing region is lost, the end can switch abruptly from growth to rapid shrinkage. This transition is called a catastrophe.

A shrinking microtubule can later switch back to growth, a transition called rescue.

The stochastic switching

growth ⇄ rapid shrinkage

is called dynamic instability.

Dynamic instability allows a cell to reorganize its microtubule network quickly without synthesizing and degrading the tubulin proteins themselves.

Microtubules are often organized from specific sites

Cells commonly nucleate microtubules at microtubule-organizing centers (MTOCs). In many animal cells, the principal MTOC is the centrosome. Microtubule minus ends tend to remain associated with the organizing center while plus ends extend outward into the cytoplasm.

This creates a polarized array that can be rapidly remodeled.

Microtubules are tracks as well as structural polymers

Motor proteins can bind microtubules and convert chemical energy into directed movement along them. Different motor families move preferentially toward one end or the other. This lets cells transport vesicles, organelles and protein complexes along defined intracellular routes.

During cell division, the same properties are repurposed: dynamic microtubules grow, shrink and search cellular space; some capture chromosomes; and organized arrays from opposite sides of the cell form the mitotic spindle.

Microtubules are therefore not rigid permanent rods. Their usefulness comes from the combination of polarity, regulated polymerization, dynamic instability and directional motor-based transport.