Horizon
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The horizon is the apparent curve that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This curve divides all viewing directions based on whether it intersects the relevant body's surface or not.
The curvature of the horizon is easily seen in this 2008 photograph, taken from a Space Shuttle at an altitude of 226 km (140 mi).
View of the ocean with two ships: one in the foreground and one to the left of it on the horizon
A view across a 20-km-wide bay in the coast of Spain. Note the curvature of the Earth hiding the base of the buildings on the far shore.
Typical desert horizon
Zenith
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The zenith is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction opposite to the gravity direction at that location (nadir). The zenith is the "highest" point on the celestial sphere.
The shadows of trees are the shortest on Earth when the Sun is directly overhead (at the zenith). This happens only at solar noon on certain days in the tropics, where the trees' latitude and the Sun's declination are equal.