Power/Toughness is a rating unique to creatures and are characteristics of that creature in all zones. It denotes numerically how strong a creature is for attacking or defending.  
Power is the first number printed before the slash on the lower right hand corner of creature cards. This is the amount of damage it deals in combat to the opposing card's toughness (or the opposing player's life, or the opposing planeswalker's loyalty).
Toughness is the number printed after the slash at the bottom right corner of a creature. It is the amount of damage needed to destroy it. If the number falls to 0 at any time, then it is put into its owner's graveyard.
Magic 2015 introduced a templating change to cards that set a creature's power and toughness to a specific value. The term base power and toughness makes it clearer that other continuous effects that modify power and toughness, such as the ones created by Titanic Growth or a +1/+1 counter, apply after the creature's power and toughness are changed.
The starter-level Portal set featured different terminology from that established in previous sets. These terms included "offense" for power, and "defense" for toughness. Although these new terms were intended to simplify learning Magic, they were a source of distress for players if and when they started to use advanced-level and/or expert-level cards, which did not use this terminology. Cards featuring these terms received errata.
A creature with higher power than toughness is considered offensive or aggressive. A creature with the same power and toughness is considered balanced. A creature with a lower power than its toughness is considered defensive.
From the Comprehensive Rules (Aether Revolt (January 20, 2017))
- 208. Power/Toughness
- 208.1. A creature card has two numbers separated by a slash printed in its lower right corner. The first number is its power (the amount of damage it deals in combat); the second is its toughness (the amount of damage needed to destroy it). For example, 2/3 means the object has power 2 and toughness 3. Power and toughness can be modified or set to particular values by effects.
- 208.2. Rather than a fixed number, some creature cards have power and/or toughness that includes a star (*).
- 208.2a The card may have a characteristic-defining ability that sets its power and/or toughness according to some stated condition. (See rule 604.3.) Such an ability is worded “[This creature’s] [power or toughness] is equal to . . .” or “[This creature’s] power and toughness are each equal to . . .” This ability functions everywhere, even outside the game. If the ability needs to use a number that can’t be determined, including inside a calculation, use 0 instead of that number.
Example: Lost Order of Jarkeld has power and toughness each equal to 1+*. It has the abilities “As Lost Order of Jarkeld enters the battlefield, choose an opponent” and “Lost Order of Jarkeld’s power and toughness are each equal to 1 plus the number of creatures the chosen player controls.” While Lost Order of Jarkeld isn’t on the battlefield, there won’t be a chosen player. Its power and toughness will each be equal to 1 plus 0, so it’s 1/1.
- 208.2b The card may have a static ability that creates a replacement effect that sets the creature’s power and toughness to one of a number of specific values as it enters the battlefield or is turned face up. (See rule 614, “Replacement Effects.”) Such an ability is worded “As [this creature] enters the battlefield . . . ,” “As [this creature] is turned face up . . . ,” or “[This creature] enters the battlefield as . . .” and lists two or more specific power and toughness values (and may also list additional characteristics). The characteristics chosen or determined with these effects affect the creature’s copiable values. (See rule 706.2.) While the card isn’t on the battlefield, its power and toughness are each considered to be 0.
- 208.3. A noncreature permanent has no power or toughness, even if it’s a card with a power and toughness printed on it (such as a Vehicle).
- 208.3a If an effect would be created that affects the power and/or toughness of a noncreature permanent, that effect is created even though it doesn’t do anything unless that permanent becomes a creature.
Example: Veteran Motorist has the ability “Whenever Veteran Motorist crews a Vehicle, that Vehicle gets +1/+1 until end of turn,” and it’s tapped to pay the crew cost of a Vehicle. This triggered ability resolves while the Vehicle it crewed isn’t yet a creature. The continuous effect is created and will apply to the Vehicle once it becomes a creature.
- 208.4. Effects that set a creature’s power and/or toughness to specific values may refer to that creature’s “base power,” “base toughness,” or “base power and toughness.” Other continuous effects may further modify the creature’s power and toughness. See rule 613, “Interaction of Continuous Effects.”
- 208.5. If a creature somehow has no value for its power, its power is 0. The same is true for toughness.
- ↑ Doug Beyer. (February 13, 2008.) "Power, Toughness, and the Flavor Thereof", Daily MTG, magicthegathering.com, Wizards of the Coast. [dead link]
- ↑ Doug Beyer. (August 17, 2011.) "The Feedbackening 2011", Daily MTG, magicthegathering.com, Wizards of the Coast. [dead link]
- ↑ Matt Tabak. (July 7, 2014.) “Magic 2015 Core Set release notes”, magicthegathering.com, Wizards of the Coast.