Pectin is a molecule similar to starch except that the repeating unit (residue) of pectin is galacturonic acid instead of glucose as in starch. Galacturonic acid is still very similar to glucose, except one of the carbons has a -COOH group attached instead of a CH2-OH. The pectin chain is held together by a bond between carbon 1 of one galacturonic acid and carbon 4 of the next one and so on. Pectinase splits the bonds between these galacturonic acids to shorten the pectin chain from large fragments in to many more small fragments. The actual catalytic mechanism introduces water so pectinase is known as a hydrolytic enzyme. It splits a water molecule and adds -H to one carbon in the bond and an -OH to the other one. Another type of pectinase also breaks this bond but by a different catalytic mechanism and is known as pectin lyase.
As you probably know, pectins are very good at binding water (pectin in jam/jelly is what makes it set), but only when the pectin molecules are quite large. So pectinase is used in industry to help increase yield of juice from fruit processing. In plants the pectin naturally functions as a "glue" to hold the cell wall together and also to "glue" cells together (the middle lamella, the bit between neighbouring cells is rich in pectin so) degrading the pectin enzymatically also makes it easier to digest the cellulose and other molecules as well as releasing water (juice).
What holds enzymes together in the first place: Enzymes are proteins and proteins are constructed from chains of amino acids (20 possible different ones). The analogy of the amino acids being like links in a chain is a good one, although it should be visualised as having 20 different types of links, all which have different shapes and properties. As an unfolded chain, the enzyme has no catalytic activity. Only the folded structure forms the catalytic or active site. However this folded structure will generally be held together by non-covalent interactions unlike the covalent bonds that hold the amino acid links together.