Modal is a type of spell spell or ability in Magic that give the caster a choice of two or more effects when they are cast. 
A modal spell or ability begins with "Choose one —" followed by multiple possible effect choices, or modes. When a modal spell or ability is announced its controller first chooses one of the modes to take effect before choosing its target or targets if it requires any. The earliest modal spell is Healing Salve, although initially it didn't have the "Choose one -" wording. It was reworded when reprinted in Urza's Saga.
There are several variations of modal spells and abilities: "An opponent chooses one —" appears on three spells, Fatal Lore, Library of Lat-Nam and Misfortune, all from Alliances. Another is called a modal replacement effect and reads "If [event], instead choose one —". This wording was used for Time Vault's Oracle text at one point, but is no longer on any cards. "Choose two -" appears on a cycle of cards (Command cycle from Lorwyn); and is given a choice of four effects, and as expected allows the user to use two of them. "Choose one or both -" has appeared a few times in the Alara block and Zendikar; two effects are given, and the caster is allowed to choose either for resolution. This is to allow flexibility if the caster prefers to use only one effect (or is forced to, for lack of a valid target for one half), while allowing the capability to perform both if required. This was an updated wording of the effects of Hull Breach, which was forced to list out all three options.
In August 2014 all cards that offer a choice were reformatted on gatherer to have bullet points. This paved the the way for the subsequent release of the Khans of Tarkir block which also featured modal spells with bullet points. 
From the Comprehensive Rules:
- Modal, Mode: A spell or ability is “modal” if it has two or more options preceded by “Choose one —,” “Choose two —,” “Choose one or both —,” or “[a specified player] chooses one —.” Each option is a “mode.” See rule 700.2.
- 700.2a The controller of a modal spell or activated ability chooses the mode(s) as part of casting that spell or activating that ability. If one of the modes would be illegal (due to an inability to choose legal targets, for example), that mode can’t be chosen. (See rule 601.2b.)
- 700.2b The controller of a modal triggered ability chooses the mode(s) as part of putting that ability on the stack. If one of the modes would be illegal (due to an inability to choose legal targets, for example), that mode can’t be chosen. If no mode can be chosen, the ability is removed from the stack. (See rule 603.3c.)700.2c If a spell or ability targets one or more targets only if a particular mode is chosen for it, its controller will need to choose those targets only if he or she chose that mode. Otherwise, the spell or ability is treated as though it did not have those targets. (See rule 601.2c.)
- 700.2c If a spell or ability targets one or more targets only if a particular mode is chosen for it, its controller will need to choose those targets only if he or she chose that mode. Otherwise, the spell or ability is treated as though it did not have those targets. (See rule 601.2c.)
- 700.2d Some spells and abilities specify that a player other than their controller chooses a mode for it. In that case, the other player does so when the spell or ability’s controller normally would do so. If there is more than one other player who could make such a choice, the spell or ability’s controller decides which of those players will make the choice.
- 700.2e Modal spells and abilities may have different targeting requirements for each mode. Changing a spell or ability’s target can’t change its mode.
- 700.2f A copy of a modal spell or ability copies the mode(s) chosen for it. The controller of the copy can’t choose a different mode. (See rule 706.9.)
- See also: entwine.