Sustain is a term that is subject to different definitions, but in the context of trial practice, it refers to a judge agreeing that an attorney's objection is valid. It usually occurs in the situation where an attorney asks a witness a question, and the opposing lawyer objects, saying the question is "irrelevant, immaterial and incompetent," "leading," "argumentative," or some other objection. When the judge sustains the objection, the question cannot be asked or answered. However, if the judge finds the question proper, he/she will "overrule" the objection.
In the context of appellate practice, if a court sustains a lower court judgment, it leaves it intact, rather than overrules it. The appeals court may sustain the original ruling, reverse it, send it back to the trial court, or reverse in part and confirm in part.