On Thursday, October 23, 2014, there will be a partial solar eclipse of the sun, and the first visible partial solar eclipse that has occurred in North America since May 20, 2012. Even more spectacularly, the partial eclipse will occur during the sunset hours on the East Coast, which should provide a fantastic visual spectacle at or around sunset. However, skywatchers in the midwest and West Coast regions will also have excellent views of the eclipse as well during the mid-afternoon hours.
What is a Solar Eclipse or a Partial Solar Eclipse? A solar eclipse occurs when the Moon passes between the Sun and the Earth during the New Moon period; and the Moon blocks the Sun from the Earth's view. During a solar eclipse, the alignment of the Moon, Sun, and Earth is as follows: Sun-MOON-Earth, with people on Earth looking back toward the SUN (Dangerous!). This is in contrast to a LUNAR eclipse, when the alignment is Sun-Earth-MOON with people on Earth looking at the MOON (Not Dangerous; the recent Blood Moons were examples of lunar eclipses). A total solar eclipse occurs when the Sun, Earth, and Moon are exactly aligned, with the Moon hiding the solar disc. A partial eclipse (which October 23, 2014's is) occurs when the Moon passes slightly out of the "line" connecting the three planetary bodies, leaving a slice of the Sun uncovered. This uncovered portion of the sun is dangerous to the naked eye.
Can I Watch the Solar Eclipse With the Naked Eye? If not, how can I watch it? As noted above, staring at the sun during a solar eclipse is dangerous and not recommended. The best way to watch the eclipse on October 23, 2014 is to do so safely, with either eclipse glasses, or with #14 welder's glass, or a similar filter. This site here does a great job on providing instructions on how to watch the eclipse safely.
When Can I See the Eclipse? The Eclipse will be at its height - meaning the sun will be the most obscured by the Moon at 6:08 PM EDT, 17:47 PM CDT, 16:35 PM MDT, or 15:15 PM PDT. There is also this handy chart here where you can look up the location, time, and amount of sun eclipsed for most major North American cities.
More Information. Earthsky has some great resources here.
Update 10/22/14: According to Slate.com, recent Solar Flares will make the eclipse better? Read Here.
Bonus Skywatching Tip for the week of October 20-25th, 2014 - the Orionid Meteor Shower. From October 20, 2014 to October 22, 2014, the Orionid Meteor Shower will be visible as well in the night skies. Even though the meteors (dust and rocks) originate from Halley's Comet, it is called the Orionid Shower because the meteors seem to originate from the constellation Orion. The peak time to view the shower is supposed to be just before dawn on October 21, 2014; when some 25+ meteors per hour may be visible in the region near Orion, as there will be no moon. Because of the dark conditions during this year's shower, it is possible that meteors may be visible through early Wednesday (October 22, 2014) morning. And, unlike the solar eclipse, the Orionid Shower will require no special viewing equipment other than your eyes! Good luck, and happy viewing!