Power of attorney gives another person the ability to act on your behalf. In trading, this means they can take over your trading accounts.
Full power of attorney is mainly used in the event that you are incapacitated in some way and need someone else to take over your complete financial affairs.
Limited power of attorney is used by portfolio managers and brokers to perform certain actions on their client's behalf. Those actions can include making trades, authorising payments and withdrawals, and acting as a proxy on some documentation.