Lens flare in anime
If you've watched anime for long you've probably seen a scene with lens flare in it, either in the form of streaks of light or as sharp diamonds. Lens flare is commonly used in beach scenes and other situations where the animators want to communicate that the sun is very bright; they'll pan a shot up to include the sun and as the sun enters the picture, throw in the flare. Generally the single callout in a single shot is the only time you'll see lens flare in the scene. As I mentioned last entry, lens flare is a really striking case of the anicamera deliberately emulating (old) cinematography for the aesthetic effect.
Here is the thing: lens flare is a lens defect and artifact, an undesirable property of camera lenses. It's not how we see bright lights with our bare eyes and it's not something that photographers want (and they go to some effort to avoid it). Old camera lenses could flare badly but modern still camera lenses go to significant effort to reduce or almost entirely eliminate lens flare; such a lens used in the same situation in real life would be unlikely to flare anywhere near as much as anime depicts (and real lens flare is often significantly less attractive than the lens flare that anime depicts).
(I don't know directly about modern cinematography lenses, but I suspect that they too do not flare very much these days; there's no reason that the improvements from still camera lenses would not have carried over to them.)
This makes anime's use of lens flare very clearly an aesthetic decision; it's not imitating how we see the world or even how a good modern camera does. Anime is doing extra work and deliberately invoking something that still photographers avoid either because the animators think it looks good, because they want things to look cinematographic (in a cliched way), or because they're using it as a signal that means 'this is in bright sunlight'.
(In anime, as in cinematography, all well lit scenes have pretty much the same apparent brightness level so true 'real world' brightness has to be communicated by other cues. Part of it is environmental, where we just know that a scene outdoors in sunlight is brighter than a scene indoors under normal artificial light, but sometimes anime throws in explicit indicators. Even artificial ones like lens flare.)
PS: this is where I direct interested parties to the tvtropes entry on false camera effects.
The unconstrained anicamera
Before I start talking about some of the things that the anicamera takes from real cameras I want to expand on a point that SeHNNG made at Altair & Vega, namely that the anicamera is unconstrained by physical reality. Specifically it is unconstrained by reality when it 'photographs' a scene, whereas when you film or photograph a scene how you do so is often imposed on you by physical constraints. There is a continuum of these constraints; the anicamera is at the unconstrained end and generally still photographers are at the most constrained end with cinematographers in the middle. This is not because film cameras are better or more flexible than still cameras but because cinematographers generally have more money. To show what I mean, here's two examples.
First, if a still photographer wants to take a picture of a group of people in a relatively small room they will almost always have to use a wide angle lens, which introduces perspective distortions from what we consider a 'normal' view. Cinematographers just build a soundstage where the room doesn't have one wall, allowing them to back up enough so that they get a normal perspective. Second, still photographers who take pictures of buildings often spend a great deal of money on special lenses in large part to compensate for the fact that they can't feasible take their pictures from ten or twenty feet (or more) up on a ladder. Camera booms are standard equipment on film sets; filming a broad overview of a building from thirty or forty feet up is almost trivial for a cinematographer.
The anicamera takes this further by enabling shots that would not be possible even in cinematography; at best film could fake them with special effects. One example comes from the first battle in Fate/Stay Night: Unlimited Blade Works, where the end of the battle has a dramatic continuous pull-back that starts from a closeup on a character in the battle and pulls all the way back to overlooking another character who is at least a mile or two away. You could not possibly film this in real life; there is no lens that could zoom in and out that much and no camera platform that could physically cover the distance fast enough. And the pull-back is necessary for the impact of the shot, because it involves Shirou turning to look towards Archer; only the continuous pullback lets us clearly understand what it means that Shirou turned and looked in the direction he did.
(Another way that the anicamera is unconstrained is that it takes up no physical space. You can thus have anime shots taken from spots in a setting that would be very difficult to get equipment into in real life. To some extent this could be faked on a soundstage but even that has limitations.)
Apart from enabling otherwise impossible shots, this matters because it means that how things look in anime is almost entirely an aesthetic choice. The look of a scene or a shot is never forced by physical constraints in the way it can be in still photography and cinematography. The corollary to this is that whenever the anicamera takes from real cameras it does so for aesthetics, admittedly sometimes because a lot of cinematography has established that those aesthetics work or at least trained audiences to expect them.
(The clearest, most striking case of this is lens flare. But that's another entry.)