A beep is a sound some horns and electronics like older computers make. My car's horn goes beep-beep!
Something is cheap if you pay less than you expect to buy it. Cheap is relative, so a cheap wedding dress can cost a lot more than an expensive meal.
Water is called deep if you cannot touch the bottom with your feet when you stand in it. Deep water can be found in the sea, or at the diving end of a pool. Wells and mines are very deep but don't always have water in them. The man in the picture is diving in some very deep water.
A heap is a large pile of similar things, making a big mound. It is also a slang word for a lot of something, for example "I have a heap of homework to do tonight".
A jeep is a fairly small, rugged, four wheel drive vehicle generally used by the military. Similar vehicles used by people outside the military are called jeeps too.
Leap is another word for jump, particularly a big jump. The woman in the picture is leaping up into the air.
A peep is a small, soft, high-pitched sound that is made by baby birds.