  We explore the properties of ionized gas in the nuclear and circumnuclear
environment of the narrow-line Seyfert 1 galaxy NGC 4051 using spectroscopic
and imaging observations from the Hubble Space Telescope (HST) and Apache Point
Observatory (APO)'s ARC 3.5m Telescope. We identify an unresolved
moderate-density intermediate width component and a high-density broad
component in the optical emission lines from the active nucleus, as well as
spatially-resolved emission extending up to $\sim$1 kpc in the AGN ionized
narrow-line region (NLR) and $\sim$8 kpc in the stellar ionized host galaxy.
The HST narrow band image reveals a distinct conical structure in [O III]
emission towards the NE, and the ionized gas kinematics shows up to two
blueshifted velocity components, indicating outflows along the edges of a cone.
Based on the emission-line image and kinematics, we introduce an improved model
of biconical outflow, with our line of sight passing through the wall of the
cone, which suggests the large number of outflowing UV absorbers seen in NGC
4051 are NLR clouds in absorption. Using the de-projection factors from the
biconical geometry, we measure true outflow velocities up to 680 km s$^{-1}$ at
a distance of $\sim$350 pc. We also map the large-scale rotation of the host
galaxy, but do not find any strong rotational component at projected distances
$\leq$ 10$"$ ($\sim$800 pc) from the nucleus. Finally, we compare the gas
kinematics with analytical models based on a radiation-gravity formalism, which
show that most of the observed NLR outflows are launched within $\sim$0.5 pc of
the nucleus and can travel up to $\sim$1 kpc from this low-luminosity AGN.
