This question came up on one of the many email lists I'm on. There were many good, brief answers; several people pointed out rightly that it's not just a matter of thinking deeply. That inspired me to write this:

Etymologically the english word "meditate" comes from roots meaning "to think deeply". Much confusion arises from adopting practices from other, vastly different cultures, and then attempting to shoehorn them into our own conceptual and linguistic structures.

There are a number of foreign words relating to the Eastern practices we're usually thinking about when we say "meditation". The one that I find most illuminating is Sanskrit "bhavana", which means something like "familiarization" or "cultivation". I asked myself the question, what is it that this word is pointing to, above and beyond concepts which I was already familiar with? Cultivation is an organic process of subtly and gently manipulating biological processes so that they gradually change into patterns that we want them to be in. So, if you want your grape vines to grow a certain way, you have to "train" them over time; and if you want your mind to work a certain way, you have to "train" it over time.

I think the most important thing, much more important than specific questions of details of one meditation practice versus another, is merely to live as if one's mind and body, one's reactions, thoughts, feelings, behavior, and so on, are all precious crops to be cultivated and improved with diligence and perseverance. God forbid one should have to reinvent agriculture from scratch; similarly, one is wise to take advantage of thousands of years of accumulated knowledge on the agriculture of the mind.

Incidentally, although the Buddhists don't talk about it so much, the Yoga Sutras of Patanjali lay out a path of cultivation that works on the body first, and then the mind. I think one benefit of this approach is that the body is more concrete than the mind, so it's easier to cultivate. Then, one can extrapolate one's experience with physical self-cultivation to mental. Of course, this is just one of many possible approaches.

The Dalai Lama says:

A note of caution is called for, however. It is inevitable that when two radically different investigative traditions like Buddhism and neuroscience are brought together in an interdisciplinary dialogue, this will involve problems that are normally attendant to exchanges across boundaries of cultures and disciplines. For example, when we speak of the "science of meditation," we need to be sensitive to exactly what is meant by such a statement. On the part of scientists, I feel, it is important to be sensitive to the different connotations of an important term such as meditation in their traditional context. For example, in its traditional context, the term for meditation is bhavana (in Sanskrit) or gom (in Tibetan). The Sanskrit term connotes the idea of cultivation, such as cultivating a particular habit or a way of being, while the Tibetan term gom has the connotation of cultivating familiarity. So, briefly stated, meditation in the traditional Buddhist context refers to a deliberate mental activity that involves cultivating familiarity, be it with a chosen object, a fact, a theme, habit, an outlook, or a way of being. Broadly speaking, there are two categories of meditation practice - one focusing on stilling the mind and the other on the cognitive processes of understanding. The two are referred to as (i) stabilizing meditation and (ii) discursive meditation. In both cases, the meditation can take many different forms. For example, it may take the form of taking something as object of one's cognition, such as meditating on one's transient nature. Or it may take the form of cultivating a specific mental state, such as compassion by developing a heartfelt, altruistic yearning to alleviate others' suffering. Or, it could take the form of imagination, exploring the human potential for generating mental imagery, which may be used in various ways to cultivate mental well-being...

http://www.mindandlife.org/dalai.lama.sfndc.html