From the events of Slumdog Millionaire, we learn very little about Jamal's mother. But from what we do know, she was an incredibly resilient individual, and a caring mother who wanted to give her children the very best lives she could.
When we meet her, she is keeping her two boys in line, fearlessly snatching them away from the policemen chasing them, and sending them off to school. From this interaction, we can infer that she has her hands full, but wants them to get the most of their education.
Of course the brothers' idyllic childhood soon takes a turn for the worse after her death in the Bombay riots. Jamal and Salim are forced to go it alone, struggling to survive as orphans. However it's clear that before she died, she was able to raise two seriously tough boys, who, in their incredible strength and resolve, almost certainly take after their mama.