赶快 (gǎn kuài) means 'quickly, at once' and carries a sense of urgency — you use it when telling someone to hurry up or when you need to do something fast. 马上 (mǎ shàng) is more neutral 'immediately', while 尽快 (jǐn kuài) means 'as soon as possible', focusing on speed without the same pushiness. 赶紧 (gǎn jǐn) is its close synonym, but 赶快 is slightly more common in everyday speech for urging someone.