The overall shape of a molecule, which generally differs between isomers, affects its physical properties. In the case of alkanes, this can be seen when the amount of branching is increased or decreased. A long, single chain of carbon atoms has a large surface area, resulting in a lot of interactions with neighboring molecules, which increases the melting and boiling points. A highly branched alkane has much less room for interaction, giving it lower melting and boiling points.
The chemical properties of a molecule also depend on the arrangement of the atoms, especially when the functional groups differ. As an example, consider propanol, with the formula CH3CH2CH2OH. An isomer of this is methoxyethane, CH3CH2OCH3. Propanol is an alcohol and undergoes very different reactions than an ether like methoxyethane.