Modern westerners approach meditation with a gung-ho goal of achieving a fierce, single-pointed that involves a highly focussed, intellectual obsession with some object that has been selected for attention. While this kind of concentration, similar to what we used to cram for an exam in our school days, can be useful for beginning to quiet a mind that wanders wildly, it isn't exactly what genuine concentration is about.
Spiritual concentration is a more refined thing. It's is not about intellectual ferocity, but comes about when a mind exists in unity and connectedness to circumstances as they actually are at the moment. Concentration is absent whenever the mind finds itself alienated from real conditions, obsessed instead with goals and outcome.
Browbeating oneself into banishing all thoughts, sweatily focussing on the breath, or a mantra syllable, or a flame, or an mental image of a lotus flower, isn't the end goal at all. This rudimentary form of intellectual concentration is useful only as a bare starting point for beginning the process of quieting the mind. It should be dropped the moment we begin to glimpse the quiet awareness beneath, which is what we're actually seeking.
What we're seeking to join ourselves to during meditation is not an object at all, but the restful, wide awake quality of bare awareness itself. A concentrated mind isn't one that lacks thoughts, feelings and concepts. It's one that is awake, present to whatever phenomena are occurring.
In practical terms for the meditator, this kind of concentration will have a more subtle feel to it. When I reach it in my own sittings, it's sometimes accompanied by a physical sensation of first becoming microscopically small, then paradoxically large. This kind of concentration feels like a fine jeweler's hammer—much smaller and humbler than a sledge hammer, but capable of far more intricate and powerful work, in the end. It's this tool, after all, that can carve diamond.