Grazing is the concept of having the player character positioned close to a bullet without actually hitting it. Depending on the game, this action rewards the player in a variety of ways; the general reward in the Touhou series is an increase of the point item value (PIV), making point items award more points. The exception to this is Embodiment of Scarlet Devil, in which graze increases the value of bullet cancels instead, as well as giving a raw score bonus at the end of every stage.
The mechanic exists in order to encourage a risk-reward style of play by rewarding the player for flirting with danger. While in some games it only exists as a minor scoring mechanism (Radiant Silvergun, Raiden Fighters series, Armed Police Batrider, etc.), some of the others base their scoring systems and sometimes even survival largely on this particular gameplay technique (Psyvariar series, Shikigami no Shiro series, Ibara Kuro: Black Label, Shuusou Gyoku and of course, the Touhou series).
In the Touhou games, grazing bonuses can make up a sizable portion of one's score, depending on the particular game and, essentially, its execution. For instance, it is very prominent in Embodiment of Scarlet Devil, where graze increases the value of cancels, the main source of points. In Perfect Cherry Blossom, grazes are performed during Supernatural Borders, especially during Spell Cards for the increased bonus, and it is the key to high scores. Imperishable Night again featured grazing as a main mechanic, as grazing during Youkai Mode will award the player time points and it is used on patterns where time points gained from grazing in Youkai Mode will outscore time points gained from shooting in Human Mode (i.e. there are many bullets, in a pattern that incentivizes grazing).
Mountain of Faith, after five mainline games in which grazing was prominent, did not reward the player for grazing in any way whatsoever, much to the disappointment of the devoted fans. However, the technique came back in Subterranean Animism, where it's once again the primary source of high scores and it has remained important throughout next releases; it is essential for scoring Undefined Fantastic Object and Legacy of Lunatic Kingdom and also notable in Double Dealing Character and Hidden Star in Four Seasons. Ten Desires on the other hand effectively made grazing irrelevant, as its unique spirit mechanic by far outscores the gain from grazing. Wily Beast and Weakest Creature once again removed the reward for grazing.
Grazing in Windows Touhou releases is usually accompanied by a sharp pop/crackle and a visualization depicting small white particles flying off from the hitbox area. Both are especially noticeable when scoring lots of graze points at once.
The technique is very effective and easy to take advantage of when combined with streaming.