Nick Bottom is the manager of the play to be performed by the 'rude mechanicals." He is extremely confident of his acting ability and feels that he can perform any role to perfection. The lines below show his opinion of acting ability:
"That will ask some tears in the true performing of it.
If I do it, let the audience look to their eyes; I will move
storms; I will condole in some measure. To the rest:--yet my
chief humour is for a tyrant: I could play Ercles rarely, or a part to tear a cat in, to make all split."
He is saying that the part he is assigned will require tears if it performed well. He also believes that he will perform it so well that he will move the audience to floods of tears as well, or at least make them feel sorrow. He then goes on to talk about the types of roles he likes to play. He really enjoys acting--especially the important or fun roles. And he thinks himself a superior actor. He is reluctant to relinquish any role to another actor because he sees himself as more capable than any other actor in the troupe.
So, in short, Bottom is a bit arrogant about his acting ability--AND--he wants any role of consequence.
See the answer by mrerick as well; it adds some important information.