Here imperative style means you can use language constructs in e.g. Python, such as if-statements and while-loops, to directly construct models. TensorFlow, Theano, and other graph-based frameworks typically require creating branches and loops as nodes in the graph.

Graphs have advantages but they can be unfamiliar and sometimes difficult:

Some advantages: easier to serialize the whole graph and distribute computation; optimization can also be performed across the graph nodes (e.g. see XLA in TensorFlow).

Some disadvantages: it can be more difficult to write and reason about, particularly for recurrent neural networks which can utilize loops a lot; also interop with reinforcement learning environments where much of the computation is performed in an environment outside of the graph.