Libertarian paternalism is the idea that policy-makers might encourage people to make decisions that are deemed good for them without mandating it. It is a way of reconciling free will with the fact that people so often seem to do things that are obviously bad for them.
Strictly speaking, this does not refer to paternalism through taxation, financial incentives, or coercion. It would not even really include limiting the options of people to those things that are good for them, like serving only healthy choices in cafeterias. Most proponents of libertarian paternalism claim that people can be guided to self-benefiting behavior through "framing." A business, for example, might allocate a certain percentage of its employees' salaries for a purely optional savings program that workers can opt out of at any time. A doctor might encourage a certain behavior (vaccination, for example) by stating the extraordinarily high number of patients who experience no negative side effects (as opposed to simply emphasizing that 2%, for example, might experience lasting side effects.)
Some forms of advertising campaigns and even government policies (Surgeon General's warnings on cigarette packs, for example) might be considered this type of paternalism. These are "soft" forms of paternalism that do not change the range of options available to people while still "nudging" them in the direction of behaviors that experts have decided are good for them.