The blue morphing cube that gives a person the power to morph. It goes by other names, but is more commonly known as the Escafil device, named after the Andalite scientist Escafil, who helped create the morphing technology.
Roughly translated as "burping DNA". Hereth illint is a process which happens if a morpher is allergic to a certain genetic pattern. It involves the morpher expelling the offensive DNA pattern while retaining their own body- the excess matter is drawn from Z-space, and the offending DNA is made into a whole new creature. 
A person who stayed in a morph passed the two-hour time limit and is trapped in that morph forever.
A strong, flexible material which can not be found on Earth, probably Andalite in origin. It can be formed into a perfect curve, like an egg-shaped to hold captives, for example, so they can't break down a wall; there are none.
Tail blade. Contemporary meaning: A close friend you never lie to and knows all your secrets. Someone you trust completely, in that they could hold their tail blade to your throat and you would never worry.
Ancient tail blade carvings.
An Andalite fighting move. It involves using the flatside of the tail blade to apply force without real injury and knocks the opponent out.
A sort of Andalite "haircut" as it were. In the ritual of Unschweet, a reprimanded Andalite is shorn of his hair so that every day he will be reminded of his shame. Each day the hair gradually grows back and with it, so grows back the Andalite's sense of dignity. Lesson learned.
A spiritual rite from Andalite legend, in which certain people with strange powers could pass memories through DNA. These memories would be triggered by imminent death to provide strength in their last moments of departure.
A disabled Andalite who can not regenerate a part of their body they lost because of a morphing allergy and is treated as an outcast and lives in isolation to retain their dignity.
An Andalite curse word.
Curiously, even though the Andalites are a telepathic species who have no need for normal speech, they have unique words and terms. It could probably be seen as a decision on the author to make the Andalites seem more alien. Alternatively, these could represent words that have no accurate English analogue.