Within Hellenic practice, miasma describes the lingering aura of uncleanliness in regards to a person or space through which contact is made with the Gods. Next to piety, being ritually clean is one of the most important things to adhere to within Hellenismos. Miasma occurs whenever the space or person comes into contact with death, sickness, birth, sex, excessive negative emotions and bodily fluids. It also comes from a lack of contact with the Hellenic Gods. As a note, I should say that not the actual acts of dying, sex and birth cause miasma but the opening up of the way to the Underworld (with births and deaths) as well as contact with sweat, blood, semen, menstrual blood and urine.
Miasma is an incredibly complicated and involved practice and it's often misunderstood--like karma. The most important things to remember about miasma is that it holds no judgement from the Gods, and that everyone attracts miasma. It's a mortal, human, thing.
In 'Works and Days', written by Hesiod, Hesiod addresses miasma and the reason for its removal as follows:
"Never omit to wash your hands before you pour to Zeus and to the other Gods the morning offering of sparkling wine; they will not hear your prayers but spit them back"
Our Gods are immortal and are sometimes called the Deathless Ones. It's our duty to uphold this sacred name by making sure no Gods but psychopomps come in contact with death even if it's through us. If we can not respect Their purity, They might be inclined to withhold Their gifts from us.
Before approaching the Gods, it's important within Hellenismos that miasma is removed. Historically, the practice of purification is called katharmos (Καθαρμός). The process of katharmos is elaborate because the process not only involves the physical but also the emotional, mental and spiritual.
The practice of katharmos historically starts with a bath (or shower, in modern times). Step two is the preparation and use of khernips (Χἐρνιψ). Khernips is created by dropping smoldering incense or herb leaves into (fresh and/or salt) water (preferably sacred spring water or sea water). When throwing in the lit item, one can utter ‘Xerniptosai’ (pronounced 'zer-nip-TOS-aye-ee') which translates as ‘Be purified’. Both hands and face are washed with khernips. The vessel holding the khernips is called a khernibeionas (Χερνῐβεῖον). For most modern day Hellenics, washing themselves with khernips is step three, seeing as they brush their teeth first, as the names of the Gods are spoken through the mouth.
Beyond the practical, there is a large mental component to katharmos. It means leaving behind negativity, worry, pain and trouble before getting in contact with the Gods. Miasma causes separation from the Gods but it's not (Original) Sin. It's not something that has to be forgiven by the Gods, except for perhaps miasma caused by murder. Miasma wears off by itself or through katharmos and it's something the practitioner has to deal with by him/herself. One may only petition the Gods with a clear mind, a clear conscience and a clean body.
The reason katharmos is as important to Hellenismos as it is, is because nearly everything in daily practice is directed at it. Study, meditation, divination, even magick. Most of it is performed to gain control over the mind and stave off self-inflicted miasma.
There are a lot of specific practices involved with katharmos; the pinning up of hair for women, sprinkling the temple area with a sprig of herbs or leaves suitable to the deity or ritual being performed, crying out ‘Hekas, hekas, este O bebeloi!’; the traditional cry of the Eleusinian Mysteries to banish any negative influence from the temple space, etc. These are important but not the main issue concerning miasma and katharmos; piety, applying khernips and regular study and meditation are far more important.