Describes something difficult to grasp, define, or understand clearly, such as a person's character, an idea, or a feeling. Often used for abstract qualities that seem to slip away when you try to analyze them.
Very similar in meaning; 掴みどころのない uses 掴む (to grab) and is slightly more physical in nuance, but often interchangeable.
Etymology
Compound of 捉える (to grasp, to catch) + 所 (place, point) + のない (there is no). Literally 'there is no point to grasp', meaning something is elusive or hard to pin down.