Min is known as the god of fertility and sexual potency but originally his fertility characteristic was not his dominant aspect. We dont know much about his original role but according to a scientific assumption he could have had a protecting feature. It is hard to see this issue clearly because his cult is not originally Egyptian. The deity may have arrived to Egypt from Nubia or Punt, the centre of his cult became Coptos. His portrayal is very typical. He appears only in anthropomorphic figure, on plain presentations always raising one of his hands and with erected phallus (the length of which always had to be traditionally 1/6 of his height. Well Egyptian deities were absolutely divine in their proportions.) :-) Above his raised hand the royal whip is visible but he never grabs that whip. This position of his hand has made scholars conclude to his protective function since such a hand-hold usually make you associate with some kind of prohibition or retaining. Looking at the Min-pictures many asked me about his missing other hand. On the portrayals indeed only his already mentioned raised hand is visible but I tell you a secret: he does have other hand too, which is clearly visible on the statues. But on two-dimensional portrayals it cant be visualised due to the concept of greatest surface, the basic characteristic of Egyptian plain-art. Take a look - Dear Reader - at this picture of statue representing Min. Here you can see his other hand that, due to its position is tightly fitting to his side. Thats why it cannot be visualised on plain surface since this hand is always at the other side of Min, opposite to the beholder.
Mins personality melted together with the Amun during the period of the New Kingdom, thus afterwards he was referred to as Amun-Min or Amun-Ra-Kamutef. Strange that though he didnt have temple or sanctuary in Thebes, he had more festivals.
Egyptians connected a special species of lettuce to Min. The relation between the plant and the deity has not been clarified yet but on the Min-processions the lettuce is carried right after the god on an altar with as great pageantry as the god himself had. According to some opinions the lettuce - as the god himself - was the symbol of sexual potency because it lets out white liquid of dense substance. Certainly this liquid of the plant used to be popular cure-all against impotency and magical medicine used for abundant offspring.