One (small animal) — the counter-pair meaning one when counting animals (typically small animals such as cats, dogs, fish, insects).
庭に黒い猫が一匹いる。
There is one black cat in the garden.
子犬が一匹生まれたので名前を考えている。
A puppy was born, so we're thinking of a name.
釣りに行って魚を一匹釣った。
I went fishing and caught one fish.
ネズミが一匹、台所を走り回っていた。
A mouse was running around in the kitchen.
A specialized/archaic textile unit — in older cloth-counting systems, '一匹' can denote a bolt equivalent to two tan (a unit for cloth). (Specialized usage.)
この反物は一匹で二反に相当すると古い記録にある。
An old record states that this bolt of cloth corresponds to two tan per ichihiki (one '匹').