A triangle is any set of three points on a plane and the lines connecting those points to each other, as long as the three points aren't all on the same line (that would just be a line). Or, you could think of a triangle as the part of the plane that lies inside those line segments. A triangle is flat - it has no thickness. But every triangle has a perimeter and an area, and three angles.
The three angles of a triangle will always add up to 180 degrees, no matter how big or how small the triangle is. Think of it this way: a rectangle has four 90 degree angles, or right angles. Adding those four angles together shows us that a rectangle has 360 degrees. But a triangle is half of a rectangle, split from corner to corner. So it has to have half the degrees of a rectangle, or 180 degrees. Because of this, if you know the measurements of two angles of a triangle, you can always figure out how big the third angle is by adding the two known angles together and subtracting that from 180 degrees.
Some kinds of triangles are more useful in math than others, and they have their own names. An equilateral triangle has all three sides the same length, like the green triangle at the top of this page. An isoceles triangle has two sides the same length (so all equilateral triangles are also isoceles triangles). And a right triangle has one angle that is exactly 90 degrees (a right angle).
To find out more about geometry, check out these books from Amazon.com or from your library: