The Moon’s orbit around the Earth is inclined by about 5 degrees from the plane of the Earth’s orbit around the Sun, so only occasionally does the Moon come between the Earth and the Sun so as to cause a solar eclipse. The diameter of the Moon as viewed from the Earth is about the same as the apparent diameter of the Sun, so the Moon can just barely cover the whole disk of the Sun. Because the Moon’s orbit around the Earth is elliptical, most of the time when there is a solar eclipse, is only partial. It is only when the Moon is closest to the Earth that the Moon can completely block out the Sun and cause complete darkness for a few minutes of totality
As the diagram below indicates, the zone of total eclipse, where the Sun is completely blocked, is very small. Only about one in a thousand people ever witness a total eclipse.
You could become one of those fortunate total eclipse viewers, if you can get to a narrow swathe across the U.S. on August 21, 2017. Around noon that day, the path of totality will run from coast to coast. A map is shown below. The next total eclipses after this will be 2019 and 2020 in Chile and Argentina, 2021 in Antarctica, 2024 in Mexico/central U.S./ eastern Canada, 2026 through Iceland and Spain, and 2027 across North Africa. The next solar eclipse with totality passing over much of Europe occurs in 2081.
All of the contiguous 48 states, as well as parts of Canada and Mexico will be exposed to a partial eclipse on August 21. Faint orange lines on the map show the limits of 90%, 75%, and 50% solar occlusion. The path of totality is only about 70 miles (117 km) wide. Below is a zoomed-in section of this map.
This site has links to this interactive map by NASA and another map from Google, and also tables of eclipse times for cities in some states. New York City, Philadelphia, Houston and San Francisco, Los Angeles, and Toronto will max out at about 70%-75% occlusion of the sun. That will be interesting to observe through eclipse glasses if the sky is not cloudy, but may otherwise be fairly unimpressive.
Totality is supposed to be a whole different experience. “Daylight is replaced by a mysterious dusk, and bright planets and stars become visible. Plants and animals act as though it were nightfall as flowers close up and birds return to roost. There’s a chill in the air because the temperature drops a dozen degrees or more. The brilliant Sun is replaced by a black orb surrounded by a ghostly halo. The colors of sunset ring the horizon…”.  “…When the shrinking visible part of the photosphere becomes very small, Baily’s beads will occur. These are caused by the sunlight still being able to reach the Earth through lunar valleys. Totality then begins with the diamond ring effect, the last bright flash of sunlight”. 
Here is a 1999 photo of the Sun being almost entirely blocked by the Moon. Solar prominences (in red) can be seen along the edge, as well as the extensive fainter filaments of the corona.
For this 2017 eclipse, totality will last about 2.5 minutes, but only near the center of the path of totality. Thus, it may be worth a little extra travel to move toward the central 40 mile wide strip. One should anticipate that many other people will be crowding into the same patch, especially if it is near a major highway, and therefore plan for traffic jams coming and going. It would also make sense to check the weather forecast a day or two before, and aim for locales expected to be less cloudy.
The safe and convenient way to look at the sun during the eclipse is with specially designed glasses.
These can be purchased for about a dollar apiece in some stores and on-line at Amazon or speciality sites . Experts warn against looking at the sun through home-made filters.
A good science project for classroom or family is to make some sort of pinhole projector, which will project an image of the Sun’s disk and which will show it being occluded. This can be as simple as a piece of cardboard with pinhole held high above a sheet of white paper on the ground, or a more elaborate box affair. Here is how to make a largish box projector into which you put your head:
This links to a short video showing how to build a small pinhole projector into a shoebox. I helped my daughter’s elementary school class make these many years ago for a partial solar eclipse. They turned out well, although the size of the projected image with this short box is pretty small. It is also possible to project a larger, clearer image of the sun using binoculars and a tripod.
 “Get Eclipsed” pamphlet, by Pat and Fred Espenak