A technical term from falconry, and in this context "taken" implies "and raised and trained." Falconry, like every other field with specialized acts and objects, has a large set of specialized terminology -- or to use the technical term, "jargon" -- and this is just one of a series describing the age when a falcon or hawk was taken from the wild: eyass, brancher (after fledging), passager (during first year), haggard (as adult). Eyass is the more common UK spelling, while eyas the more common in the US. Like most falconry terms, it dates to the middle ages, in this case borrowed from French niais, nestling (from Latin nīdus, nest) and then converted from a nyas to an eyas (following the same process that turned a nuncle to an uncle).
I know Bob simply dotes of his new eyass, but dang it, birds just do not look good when their feathers are first coming in.