Erection is the word used to describe the state when the penis becomes hard. 

The penis consists of erectile tissue, which can become filled with blood and swell up, which is what happens when you get an erection. The erectile tissue continues some way into the body and can be felt between the scrotum and anus. The penis is therefore not a muscle and it cannot be exercised or stretched in order to be made bigger. In an erect state, a penis may be curved in one direction or another but it can also be more or less straight.

You may get an erection from sexual fantasies and dreams, or from different impressions such as smells, tastes or pictures. You can also get an erection if your penis is caressed, stimulated manually or exposed to vibration. You can also often get an erection 4-6 times during the night; this is a bodily activity that happens automatically.