Microtubules are made from a protein called tubulin. They can function to support cell shape, help cell division, can be used as tracks to transport vesicles across the cell and also can function in cell movement, since they are part of cilia and flagella.
Microfilaments are thin fibers that are part of the cytoskeleton. They provide structure and shape of the membrane. They are also responsible for protrusions of cells, such as: lamellipodia, microvilli etc. Microfilaments can form contractile bundles and help cell motility. Macrophages, neutrophils and mast cells use microfilaments for motility. Special Bands of actin and myosin (in development) help cells contact and bend into structures like Neural tube.