A plasmid is an extra-chromosomal element, often a circular DNA. The plasmids we will use in this class typically have three important elements:
An origin of replication
A selectable marker gene (e.g. resistance to ampicillin)
A cloning site (a place to insert foreign DNAs)
Since a plasmid is (by definition) an extrachromosomal element, it cannot make use of any origin of DNA replication in a chromosome. That is, DNA synthesis within (i.e. copying of) a plasmid depends on its having an origin of DNA synthesis of its own. Obviously, if a plasmid couldn't be copied, it would be rapidly diluted out in a population of dividing cells because it couldn't be passed on to daughter cells.
A selectable marker is not actually a required element of a plasmid, but it makes it possible for us to maintain stocks of cells that contain the plasmid uniformly. Sometimes, carrying a plasmid puts a cell at a selective disadvantage compared to its plasmid-free neighbors, so the cells with plasmids grow more slowly. Cells that happen to "kick out" their plasmid during division may be "rewarded" by having a higher rate of growth, and so these plasmid-free (sometimes referred to as "cured") cells may take over a population. If a plasmid contains a gene that the cell needs to survive (for example, a gene encoding an enzyme that destroys an antibiotic), then cells that happen to kick out a plasmid are "punished" (by subsequent death) rather than "rewarded" (as in the previous scenario). That selective pressure helps to maintain a plasmid in a population.
A cloning site is not required at all, but it sure is nice to have! What I mean by "cloning site" is a place where the DNA can be digested by specific restriction enzymes - a point of entry or analysis for genetic engineering work. This is a matter we will be discussing in great detail at a later point. For now, think of the following example: Suppose you are really thirsty and you buy a can of soda. Does it occur to you that one end of the can (the "top") is designed so that you can open it easily? If you bought a can of soda with two bottom ends and no top, you would have a hard time drinking it! It's the same way with plasmids. You can have a plasmid with lots of terrific features, but you might lack an easy way of "getting it open" with restriction enzymes.
You probably remember that double-stranded DNA has the form of a "double helix" which looks a bit like a telephone handset cord (except that the telephone cord is a single helix). You may also recall that the double helix is right-handed (for an expose on the difference, take a look at the Left Handed DNA Hall of Fame Site.)
You've probably also noticed how knotted up a telephone cord can get, if your roommate twists the handset around a few times before hanging up. Those knots are a higher order structure that lead to "coiled coils."
DNA has the same problem, though your roommate isn't to blame this time! Aside from the double-helical structure that we all know and love, DNA can take on a higher order coiling that twists one double helix around another. We call this "superhelical coiling" or simply "supercoiling." In a linear molecule these twists can unravel by themselves, provided the ends are not prevented from rotating. In a circular molecule with no free ends, the superhelical twists are "locked in" and the molecule cannot relax. This coiling is not the same as the right-handed double helix coil with which you are all familiar. The supercoiled molecule is a coiled coil.