Muggles' Guide to Harry Potter/Magic/Squib

Overview
The opposite of a Muggle-born witch or wizard, a Squib is the child of wizarding parents with no magic powers of his or her own.

Extended Description
Squibs live a most uncomfortable life. Raised in Wizarding families, they are perforce aware of magic, and see it used all around them all the time, and yet they cannot take part in it. While the Ministry of Magic shields Muggles from this awareness of the magical world, nothing can be done for Squibs without depriving them of their parents; they would have to forget the entire time they were growing up, when magic would have been pervasive in the family home. It is quite likely that this deprivation of magic leaves most squibs embittered.

On the Hogwarts Express in his first year, Ron Weasley mentions that he has a relative who has no magical abilities; he believes she is an accountant, but says that they don't talk about her much.

During Harry's second year he discovers that Filch is a Squib. We also learn that there are mail-in courses that are supposed to teach magic to squibs; the effectiveness of these courses is unknown, but the author has stated, in a later interview, that the home-study course does not work on Filch.

Before the start of Harry's fifth year, Arabella Figg reveals to Harry that she is also a Squib.

Neville Longbottom is initially so unsure of his magical abilities that he is afraid that he is "almost a Squib".

There are rumours that Professor Dumbledore's late sister Ariana was hidden away from Wizarding society because she was a Squib and an embarrassment, rumours that are fanned by Rita Skeeter in her "tell-all" book about Dumbledore, which was published shortly after his death. It is worth noting that squibs not only had a hard life, as mentioned above, but were embarrassments to their parents.

Analysis
Early on, we learn that not all wizards are equally powerful. Quite apart from the obvious specializations – Madam Pomfrey Healing, Madam Hooch with flying and refereeing, and Professor Snape with his Potions, to give a few examples – we gather that there are wizards who overall have stronger or weaker magical abilities. This is explicitly mentioned several times in the case of Neville Longbottom, who repeatedly bemoans his magical weakness. We also learn that it is possible for wizards to spring from Muggle families, and we are presented with Hermione Granger, who has done exactly that. Combining these two, it is clearly possible that a Wizarding family may, on occasion, contain an individual with limited or no magical powers. While Ron touches on the concept briefly, and Neville more strongly, we don't hear the name for the condition until Harry's second year.

Despite their lack of magical ability, Squibs are now regarded as part of the Wizarding world. This is a very uncomfortable place for them, as they are perforce aware of the world of magic but cannot join it. All the same, it is better than the past century, when they were apparently often hidden away as being unfit for either Wizarding or Muggle company.

It is perhaps worth mention that while "Squib" is a term for non-magical people born of magical parents, there is no analogous term for magical children born of Muggle parents (like Hermione, whose parents are both Muggle dentists). The closest term available is "Muggle-born", which seems to be used only as a term of derision, a milder form of "Mudblood".