What does the cytoskeleton do?
Majorly three types of cytoskeletons exist in eukaryotic cells namely Microfilaments,Microtubules and Intermediate Filaments.
For Prokaryotes it's bit different.(Not going in details about their histology as the question doesn't ask about it)
Roles of Cytoskeletons
They provide cells a particular shape(Remember one thing that we often say animal cells have got no specific shape but it is said because in an animal's body variety of cells exist which require different shape based on their function and location and it is the cytoskeleton which gives that required shape)
It divides the cell cytoplasm in to several compartments so that various metabolic processes can be executed at the same time without any interference.
It provides cellular organelles necessary support for their intracellular movement.
It helps in different endocytosis or tranaport processes.
An example is Neurofibrils help to maintain uphill and downhill transport of important substances in the neurons which is attacked by abnormal tau proteins in Alzheimer's disease that leads to neural beads formation which is the inactive form of these Neurofibrils
It forms various specialised structures like flagella for motility.
In lower eukaryotes like nematodes it forms the basis of glucose uptake and utilization.(Hence drugs like Benzimidazole eg Albendazole, targets this cytoskeleton to kill ascaris like nematodes.)