The qualifier 'free' seems to be ubiquitously attached to discussion of radicals as highly reactive species with unpaired spins. What, precisely (or imprecisely, as the case may be) does 'free' really mean?
Free as in free speech? Free beer? Freedom of movement? Kinetic accessibility?
I liked this question because I had never thought much about it. However, it's not such a mystery because the answer is on Wikipedia's “radical” page:
Historically, the term radical was also used for bound parts of the molecule, especially when they remain unchanged in reactions. These are now called functional groups. For example, methyl alcohol was described as consisting of a methyl "radical" and a hydroxyl "radical". Neither are radicals in the modern chemical sense, as they are permanently bound to each other, and have no unpaired, reactive electrons. However, they can be observed as radicals in mass spectrometry when broken apart by irradiation with energetic electrons.
So, the free in free radical was originally used to distinguish it from a radical bound to a carbon skeleton.
Digging into historical chemistry texts reveals that “free radical” becomes really widely used around 1930:
However, some quotes for earlier works use it, though it does not appear so frequently that it may be considered a common expression. In other words, at that time simply the juxtaposition of the adjective free with radical, became synonymous with group (or today's noun substituent). For example:
“This hydrocarbon was formerly supposed to be the free radical of the methyl group, but no methyl compounds have in any way been derived from it, whilst by the action, of chlorine upon it, ethyl chloride is obtained as the product” (1870, Lessons in elementary chemistry)
or
“Although, however, the free radical methylene is unknown, many of its compounds have been prepared, of which some, such as the haloid ethers, &c.” (1884, A Treatise on Chemistry, Henry Enfield Roscoe and Carl Schorlemmer)
Though more quotes could be dug and provided, the ones I've read support this idea that free radical initially meant “the chemical group as a molecule by itself”.
TLDR; It depends who you are talking to (organic chemist, ESR spectroscopist, or physical chemist/chemical physicist), and when.
The way I read the quote below the fold, there have been three major senses of the definition, at least to the best of the knowledge of a giant in the field like Herzberg:
The sense as described by Terry Bollinger, where an entity that in modern terms is described as a functional group (HT: F'x) is found to be stable as an isolated entity.
Free in this case refers to the chemical stability of the species, while radical is used in the older sense of the term indicating a 'fundamental chemical unit'.
The sense as might be used by an ESR spectroscopist, encompassing any systems bearing nonzero electronic spin.
Free in this case carries the sense of 'available for measurement by spin resonance techniques,' and radical is used in the newer sense, indicating the presence of nonzero electronic spin.
The sense defined by the 'chemical transiency' of species that are chemically short-lived but physically stable (possess a nonzero dissociation energy), regardless of their electronic spin.
Free here refers to 'detached transiently from a more stable system,' whereas radical hearkens back to the older sense of the term, meaning a 'fundamental chemical unit.'
I'm pretty sure Gerhard Herzberg is a reliable source. I will quote (extensively!) from the introduction to his 1971 Spectra and Structures of Simple Free Radicals, since he says it far better than I could (all emphasis is in the original; bracketed ellipses are my elisions, un-bracketed ellipses are original):
The concept of a radical in chemistry is a very old one; it goes back to Liebig. Quoting an old [1884] text book of organic chemistry, "Radicals are groups of atoms that play the part of elements, may combine with these and with one another and may be transferred by exchange from one compound into another." Free radicals first came to be considered after Gomberg at the turn of the [20$^\mathrm{th}$] century observed triphenylmethyl to be a chemically stable system. However, simpler radicals like $\ce{CH3}$, $\ce{CH2}$, $\ce{CH}$ are extremely short-lived species, difficult to produce and study in the free state. They are chemically unstable even though in general they are physically stable; that is, if undisturbed by collisions they do not spontaneously decompose: they have a nonzero dissociation energy.
According to the quantum theory of valence a group of atoms (a radical) when split off a parent molecule often has one or more unpaired electrons—that is, has nonzero spin $\left(S\right)$. This circumstance has led many authors, particularly organic chemists, to define a free radical as a system with nonzero spin. Such a definition is particularly convenient for those working in the field of electron-spin resonance, since it implies that all systems and only systems that can be investigated by electron-spin resonance are free radicals. While such a definition is extremely simple and straightforward, it does have two drawbacks: according to it certain chemically stable molecules such as $\ce{O2}$, $\ce{NO}$, $\ce{NO2}$, $\ce{ClO2}$ must be considered as free radicals, while on the other hand quite a number of systems that are highly reactive and short-lived, such as $\ce{C2}$, $\ce{C3}$, $\ce{CH2}$, $\ce{CHF}$, $\ce{CF2}$, $\ce{HNO}$, $\ldots\,$, in their singlet states $\left(S=0\right)$ are not considered to be free radicals. Indeed, one and the same system, such as $\ce{CH2}$, would or would not be a free radical depending on the electronic state in which it happened to be. [...].
Therefore many physical chemists and chemical physicists use a somewhat looser definition of free radicals: they consider any transient species (atom, molecule, or ion) a free radical—that is, any species that has a short lifetime in the gaseous phase under ordinary laboratory conditions. This definition excludes $\ce{O2}$, $\ce{NO}$, $\ldots$ but includes $\ce{C2}$, $\ce{CH2}$, $\ce{CHF}$, $\ldots$ even in singlet states. It also includes atomic and molecular ions. [...] While most of the free radicals that we shall be discussing have lifetimes of less than a millisecond, we must realized that there is no sharp boundary; indeed, some of the radicals we are including have lifetimes of about $0.1$ sec.
A radical is a group of atoms that tend to stay together and act as a persistent chemical unit in reactions. The methyl group $CH_3$ is a common example. My own favorite radical is ammonium $NH_4$, which behaves strikingly similarly to an alkali metal such as lithium or sodium, so much so that you can even create amalgams of ammonium with mercury.
A free radical is what you get if the radical group is capable of existing on its own. The ammonium radical is an example, and one of the more stable ones. Methyl can be free also, but tends to be far more reactive and so shorter lived.
Free radicals always have "dangling bonds," since they are by definition parts of larger molecules that have been broken off of those molecules. However, that doesn't mean they are any more reactive than are free elemental atoms, ammonium again being a good example.
