The basic idea of filtering recognises that writers very often use phrases which get between the reader and a straightforward representation and evocation of what's happening, without adding anything else to the experience. John Gardner (as far as I know) originated the word, and describes it thus:
... the needless filtering of the image through some observing consciousness. The amateur writes: "Turning, she noticed two snakes fighting in among the rocks." Compare: "She turned. In among the rocks, two snakes were fighting ..." Generally speaking - though no laws are absolute in fiction - vividness urges that almost every occurrence of such phrases as "she noticed" and "she saw" be suppressed in favor of direct presentation of the thing seen.
I sometimes liken filtering to showing the reader your story through a periscope: they are constantly reminded of the lens through which they're looking. And getting rid of filtering is one of the simplest ways to make your writing more vivid and engaging, because it doesn't change anything about plot and story, and very little about voice. I've blogged more fully about it, so this is a quick look at the issues that most often arise when I'm teaching how to wrangle it.
1) It's not the "filter words" themselves that are the problem. Yes, words like looks, sensed, remembered, decides, noticed, sees, seemed, finds, think, recalled, perceives, observed, watching, wondered, considers, are pointers to the fact that you're showing the reader your story through a filter. But such words are not a problem in themselves: they are not Bad Words, any more than was is a Bad Word. In fact, I'd be extremely surprised if you could write a story without using at least some of them. You don't cut these words because you "shouldn't" have let them into your draft in the first place: they're simply the canary in the mine, telling you there's a phrase which is creating that sense of padding, that veil between the reader and the story-world and its events. Assuming it is doing that, of course, because …
2) … sometimes you want to remind the reader of the consciousness through which we're perceiving and experiencing the scene, whether that's a character's perceptions in the moment, or a narrator or a character's more distanced, contextualised telling of the story. If the point of the sentence is a sudden, important realisation, then "realises" is possibly going to be the best way to make that point. For what it's worth, when I perform a "filterectomy" I find that 75-80% of the filtering gets cut, and the remaining fifth to a quarter of it turns out to be very much earning its keep in the storytelling.
3) First-person narrators are particularly prone to filtering. When an internal character-narrator is telling their own story, you-the-writer are very aware of working through their viewpoint: where their eyes are directed and how their mind is processing the events around them. In first draft that tends to end up on the page, but it's an easy fix: just schedule a filterectomy. Some beginner writers assume that writing in third person, with an external narrator, has a more distancing effect, but although viewpoint is still crucial in controlling the reader's experience, some writers find it easier to Show what's happening, without intervening reminders of who's doing the perceiving, when they're not tied to a specific character's moment-by-moment experience.
