I came up with the following cognitive science definition of mindfulness based on Stanovich’s Rationality and Reflective Mind  which I am reading:
Mindfulness = being able to suppress the algorithmic mind from creating secondary representations of the world and engaging in cognitive simulation
In normal language, I would define mindfulness as:
The state of being present in the now, accepting all that is unfolding without trying to change anything or being attached to the hypothetical scenarios arising in the mind
Stanovich introduces a tripartite theory of the mind in his book. In the tripartite theory, the mind consists of the following modules:
- Autonomous mind: heuristic, fast, intuitive, subconscious mind. Comprises of the autonomous subprocesses that execute automatically based on current stimuli
- Algorithmic mind: A module which processes information analytically and makes calculations with a set goal. Processing is conscious. Responsible for sustaining decoupled secondary mental representations of the world, which are formed on the basis of the primary representation of the world that is generated automatically by the autonomous mind, and the cognitive simulation and hypothetical thinking, which are done based on these secondary representations
- Reflective mind: a module that decides when to suppress processing and reactions based on autonomous mind and begin cognitive simulation activites in the algorithmic mind
Nowadays large and increasing proporition of people work in jobs that require analytical thinking. Analytical thinking means using reflective mind to initiate analytical processing in the algorithmic mind when necessary. Because behaviors that are repeated tend to become automatic, commencing cognitive simulations and hypothetical thinking in the the algorithmic may become automatic or habitual for many people. This means, a large number of people are automatically starting cognitive simulations and hypothetical thinking even when it is not needed or good for them. Thus, mindfulness becomes a goal.
Our reflective minds need to learn also to override the too-easily-triggered cognitive simulations in the algorithmic mind. How? Meditation. In meditation you specifically train your reflective mind to stop the algorithmic mind from running amok with all the hypothetical thinking and return to the primary representation of the world: the Now.