First, let's get the obvious out of the way. Timescape is a coinage—that is, a newly created word. Basically, Gregory Benford took such words as landscape, seascape, and townscape and modified a new word from them: timescape.
A seascape is a portrait or scenic view of the sea and a townscape is a portrait or scenic view of a town. Similarly, through its title, Timescape promises its readers a portrait of time.
But what does it mean to view time? Through the characters' scientific efforts, folks like Markham, Renfrew, and Gordon all manage to catch glimpses at a new way to view time. For them, time is no longer a series of chronological events, where A happens and then B happens, but instead, time exists as part of the composition of the universe (read: spacetime).
As we said, characters only manage to catch glimpses of the timescape, but at the novel's end, Gordon has perhaps the most comprehensive view of it when he thinks:
But they were all simply figures. A piercing light shone through them. They seemed frozen. It was the landscape itself which changed, Gordon saw at last, refracted by laws of its own. Time and space were themselves players, vast lands engulfing the figures a weave of future and past. There was no riverrun of years. The abiding loops of causality ran both forward and back. The timescape rippled with waves, roiled and flexed, a great beast in the dark sea. (46.93)
The above quote includes the only mention of the word timescape in the novel. Along these lines, the definitive meaning of the timescape is never expressly outlined. That said, we can glean certain clues about it from the above. The timescape is not simply the universe, but a type of dimension that includes the past, future, and present all wrapped up together. Also, cause and effect have less meaning in the timescape—as proven by Renfrew's experiment, information can be sent back in time, meaning the effect can occur before the cause in the "loops of causality."
Ultimately, Gordon thinks of the timescape as a type of "great beast in the dark sea." The dark sea imagery is important here. Even though Gordon and other scientists can visibly see the effects of the rippling waves, ultimately, they remain in the dark as to what exactly the timescape is. Even by the end of the novel, further investigation, experimentation, and theorizing are required before the true nature of the timescape will open itself up to humanity.