Deliberative means carefully thought through or discussed. A jury meticulously considering all the evidence before reaching a verdict is one example of a deliberative process.
If your mom is offered a great job in another country, she may respond immediately, but she's likely to be more deliberative, going over the pros and cons of moving far away for work that she loves. When you do something deliberative, you deliberate, carefully weighing all the options before making a decision. The Latin root deliberare means "consider carefully," or literally "weigh well."