What is the mechanism of a competitive inhibition?

Because when there is a competitive inhibitor present (i.e. a substance which competes with the 'correct' substrate for a place within the enzyme active site), that means that the reaction proceeds more slowly (at a lower rate) for any given substrate concentration.

More substrate is required to successfully 'saturate' the enzyme present, and minimise the effect of the inhibitor, i.e. the Michaelis-Menten curve gets less steep, and reaches an asymptote (Vmax) at a point further towards towards the right hand side of the graph (at a higher substrate concentration).

Since Km is the substrate concentration at half-Vmax, Km also gets shifted to the right, i.e. it increases.