Polymer

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A polymer is a kind of complex molecule. Each polymer is made up of one or more simple molecules which are linked into a complex, possibly repeating structure.

Polysaccharides

Polysaccharides polymers of sugars. For example, cellulose is a common polymer in plants (often just called "fibre" by the food industry). Plants create cellulose by reacting glucose molecules with one another to link them into a long chain.
Polysaccharides can be described in terms of which sugars they are made from, how adjacent sugars are oriented relative to one another and which of their carbon atoms take part in the link. In essence, a link is an alpha-link if the OH-group is on the opposite side of the ring's plane from the rest of the sugar, while it is a beta-link if on the same side^[1]. (To do: I will add an illustration. It is difficult to understand otherwise.) The carbon atoms to which an adjacent sugar can bond are numbered, so cellulose can be denoted as a chain of glucose with $\beta (1\rightarrow 4)$ links.