。
The neighbor's dog is always barking.
Literal
Next [of-の] dog [topic-は] bark-て only is-ing.
~てばかりいる ('is doing nothing but X, keeps on X-ing') is a pejorative continuous pattern — complains that the subject does X to the exclusion of everything else. ばかり ('only, nothing but') is the limiting particle. Standard complaint about noisy neighbors.