Those are coats of arms whose blazon, or verbal description in the language of heraldry, recalls the name (or, less often, some attribute or function) of the holder of the arms.
Canting arms (armes parlantes in French) are extremely common. The medieval mind was quite fond of puns, but at a more basic level, arms were a form of visual identification in a world of limited literacy, and it was perfectly natural for someone to use as his emblem a device which recalled his name.
A visual pun (a combination of objects whose names can be used to form a name or phrase) was a common medieval pastime, called rebus (Latin = with objects). A simple rebus would be one where one object is sufficient to form the pun.
Perhaps the most famous example is provided by the arms of the Spanish kingdoms of Castile (Gules a castle or) and Leon (Argent a lion purpure). Here, the main (or sole) charge recalls quite obviously the name of the bearer. In both cases the charges happen to be among the most common in ordinary heraldry. In many cases, unusual or rare charges have been introduced into heraldry for the main purpose, it seems, of being able to pun on the name of the holder.
Sometimes more than one charge is needed, or more than one word to make the pun apparent.
The allusion can be more indirect.
Pursuant to the edict of 1696, in France, many people were forced to acquire coats of arms whether they wanted them or not, so the king could collect the registration fee. As a result, the heralds allowed themselves to inflict punning arms on many of their hapless victims, especially members of the legal profession. The notary Pierre Pépin in the Nivernais was given Argent three stones of grape sable (= pépin in French). Philippe de La Folie, notary in Burgundy, was given a Harlequin proper. An apothicary in Brittany was given Azure a clyster between three chamber-pots argent. A parish priest near Nevers was named Joseph Bonnamour, and he received Azure a Cupid argent holding in his hand a heart inflamed gules. In Normandy, a fellow named Alexandre Le Marié was given Gules a stag's attires or (horns being the traditional attribute of the cuckold husband!). (These, and other examples, from Rémi Mathieu: Le Système héraldique français, 1946).
Many cants are not obvious because they use either an unfamiliar language (Avaugour in Brittany bears an apple-tree, for aval gor meaning crab-apple in Britton), or a word which has disappeared from the common language (Fouquet bears a squirrel, whose name in Middle French was fouquet).
In a few coats, a ticnture was enough to make the pun, and the arms were chosen to be of the tincture, without any charge whatsoever:
I presume that Blanc de Simiane (quarterly argent and azure) and Blanc de Blanville (quarterly per saltire argent and azure) have canting arms.
Some puns are more subtle, and involve the blazon itself rather than the charges. In other words, they would be incomprehensible without a knowledge of the proper heraldic terms.