一齐 emphasizes simultaneity - things happening at the exact same moment. Compare with 一起 (yīqǐ) which means 'together' and doesn't necessarily imply doing things at the exact same time.
usage
齐 alone means 'neat/uniform/even.' 齐心协力 (qí xīn xié lì) = 'working together with one heart' - a common idiom for teamwork.
