A right triangle is any triangle where one of the angles is exactly 90 degrees, or a right angle. You can't have more than one 90 degree angle in a triangle, or it would be a rectangle. In a right triangle, the side opposite the right angle has to always be the longest side, and the two other angles both have to be acute.
The perimeter of a right triangle is the same as any other triangle - you add the lengths of the three sides together. To find the area, imagine that you have two of these triangles exactly the same. Flip one upside down and put its long side against the long side of the first triangle; now you have a rectangle. Multiply the length by the height of the rectangle to get the area of the rectangle. Now divide that in half again to get the area of one right triangle.
But the really cool thing about a right triangle is that if you know how long the two shorter sides are, you can figure out the length of the long side. You do it using the Pythagorean Theorem.