If something is concise, it's short and gets right to the point. A concise edition of your diary might be 50 pages of the most important entries.
Concise comes from the Latin word concidere, which means to cut down. When we use concise, we're talking about words that have been cut down. There are no concise trees, but there are concise works of political philosophy. A concise Italian-English dictionary, is shorter than an unabridged one. If you're good at quick explanations, you have a concise manner. A good synonym is succinct.