Hypertrophy is the sole phenomenon of muscles getting bigger. (This can be considered a distinct physiological process, but is difficult if not impossible to trigger separate from increases in strength, endurance, and so on.)
Hypertrophy in and of itself slightly increases strength due to leverage advantages that come with greater cross-sectional area producing a superior angle of contraction.
Hypertrophy in and of itself says nothing about flexibility. Hypertrophy training can result in reduced or increased flexibility; this is determined by the program one uses.
Hypertrophy alone may create greater metabolic demand, that is, it's harder to fuel a bigger body during sustained cardio effects. But other training can obviate this effect.
But all in all, hypertrophy gets a bad rap. Excessive attention on bodybuilding in popular Western culture has caused lifting weights to be associated with bodybuilding's excesses, but the fact is that hypertrophy should generally be desired by everyone. It's a rational goal of working out that carries vanishingly few negative effects of any significance at all.