Complex sentence: On a Lorentzian manifold, certain curves are distinguished as timelike, and two timelike curves are said to be timelike homotopic if there is a homotopy between them such that each intermediate curve is timelike.
Split into simpler sentences: On a Lorentzian manifold, certain curves are distinguished as timelike. A timelike homotopy between two timelike curves is a homotopy such that each intermediate curve is timelike.