Motivation is an individual's willingness to show effort
toward achieving a goal
. That's the simple definition.
A more complicated (but more accurate) definition would go like this: Motivation is an individual's self-conception of their ability to meet various needs... as that ability impacts upon the individual's ability to achieve a larger goal. Motivation can therefore be intrinisic or extrinsic, or both: it's all about how one's ability to do small things affects their ability to do big things.
Back in the day (a few decades ago), there were basically two predominant theories of motivation. Abraham Maslow devised Maslow's Hierarchy of Needs, which stated that an individual would be motivated to meet external (physiological and safety) needs before internal (social, self-esteem, and self-actualization) needs. Frederick Herzberg came up with the Motivation-Hygiene Theory, which said that external factors would lead to dissatisfaction, while positive internal factors would lead to satisfaction. Both theories have since been declared bunk by most management scientists, but they are still popular ways to conceptualize motivation.
Here are the various theories of motivation we have in the contemporary debate:
Expectancy Theory: states that motivation is a function of three variables: expectancy (faith in one's own performance), instrumentality (perceived importance of effort), and valence (perceived value of the outcome).
Equity Theory: posits that an individual is motivated by a perceived output greater than perceived input, in comparison to other individuals. In other words, people do things when they expect to do better, with less effort, than the others around them.
Goal Setting Theory: essentially proposes that motivation is driven by goals, and that performance is generally dictated by the scope of the individual's goal, as well as self-efficacy and other minor factors.
Reinforcement Theory: states that behavior is caused by external factors—conditioning. Motivation is caused by reactions to past consequences of past actions.
Three Needs Theory: refers to the need for achievement, power, and affiliation. Each individual is said to pursue each need in varying degrees. An engineer probably pursues the first, a politician probably pursues the second, and a salesman probably pursues the third (although there's plenty of variance, of course).
So that's motivation. You really should get some: it's good stuff.