So full of energy, cheerfulness, and confidence that nothing can hold it down. To repress something is to push it down and keep it from coming out; 'irrepressible' says the pushing does not work. It describes people — an irrepressible child, an irrepressible host who keeps the whole table laughing — and also feelings that keep bubbling up: irrepressible laughter, an irrepressible grin, irrepressible optimism. It is warm and admiring when used of a person, though it can carry a light 'this one is a handful' feeling too, the way you might say it about a lively student. It is a fairly formal, written word, and you meet it most in profiles, obituaries, and sports writing. Note that its parent word 'repress' is usually negative (repress a people, repress a memory), so the whole word carries a faint sense of spirit that refused to be crushed.