The pH of a solution is determined by the concentration of hydrogen ions (H+) in the solution. A weak acid is an acid that partially dissociates in water, meaning that only a small fraction of the acid molecules donate a hydrogen ion to water. This results in a solution that has a higher concentration of hydrogen ions than pure water, but not as high as a strong acid.
A weak base is a base that partially dissociates in water, meaning that only a small fraction of the base molecules accept a hydrogen ion from water. This results in a solution that has a lower concentration of hydrogen ions than pure water, but not as low as a strong base.
In the case of a solution with a pH of 10.1, the solution is basic because the concentration of hydrogen ions is lower than in pure water. This means that the solution contains a higher concentration of hydroxide ions (OH-), which are responsible for the basic properties of a solution.