It is the same paint you're familiar with: "A coloured substance which is spread over a surface and dries to leave a thin decorative or protective coating." (Oxford Dictionary)
When you apply paint, it goes on as a liquid. Once it dries, it becomes a solid coating/covering.
So, when paint begins to come off of a surface, it does so in small, solid chunks, which are called "flecks".

(Flecks Of Paint, Essaouira, by Antony Stanley from Gloucester, UK, courtesy of Wikimedia Commons)
One of these flecks of paint—a tiny piece of debris—hit the spacecraft with such rapid velocity that it caused more damage than one would naïvely expect from its small size.
In 1983, during the launch of the space shuttle Challenger, a tiny fleck of paint hit the windshield with such a velocity (> 20,000 km/hr) that it created a pit (indentation).