carbon skeleton
Picture a molecule as a body: the carbon skeleton is its bones, the framework of carbon atoms chained and ringed together that everything else hangs on. Mentally erase the functional groups from any organic molecule and what remains — the connected web of carbons (and the hydrogens that fill them out) — is the carbon skeleton, also called the carbon framework or backbone.
The carbon skeleton is the arrangement of carbon-carbon bonds that defines a molecule's basic shape: straight chains, branched chains, and rings, in any combination. Carbon's ability to form four strong, stable bonds and to link to itself almost without limit (a property called catenation) is exactly what makes such elaborate skeletons possible — and that is why carbon, almost uniquely, can be the scaffold of millions of compounds. Chemically, the skeleton is mostly the quiet part of the molecule: the C-C and C-H bonds are strong and nearly nonpolar, so the skeleton itself usually does not react under mild conditions. It mainly sets the size, shape, and rigidity, while the functional groups bolted onto it do the reacting.
Splitting a molecule into skeleton plus functional groups is one of the most useful habits in organic chemistry. When you name a compound, you find the parent chain in the skeleton; when you plan a synthesis, you often build the skeleton first and install the functional groups onto it. Thinking this way lets you see a daunting structure as something familiar — a known skeleton wearing a few known groups.
Butane, 1-butanol and 1-bromobutane all share the same four-carbon straight-chain skeleton (C-C-C-C); they differ only in the group at the end — nothing, an OH, or a Br — which is what gives each its distinct chemistry.
One shared four-carbon skeleton, three different functional groups, three different compounds.
The skeleton sets shape and size and is usually the unreactive part; the functional groups attached to it drive the chemistry. The two ideas are complementary, not competing.