An entry of appearance is a lawyers way of entering as counsel in a case. It is a representation that he or she represents a party. Waiver of summons means that a party voluntarily enters a lawsuit without requiring the opposing party to serve them with a summons and petition (have the sheriff or process server physically hand you the lawsuit). Waiver of notice of hearing means that you consent to a hearing happening without notice or sufficient notice to you.
I would not accept these papers or sign any ratification. Husband needs to demonstrate that you were served with a Petition for Dissolution to the court before he can move forward with the divorce. You cannot be expected to knowingly enter if you do not have a copy of the lawsuit. You should never waive any rights unless you understand what those rights are in the first place.
You should not sign any documents given or mailed to you by your husband or his attorney without first seeking legal advice. Many spouses and their attorneys attempt to streamline the divorce process by first getting the other party to waive the service of the petition, and may at the same time include a waiver of your right to appear in court and contest your husband's demands. Without knowing if he has made fair provisions for the custody and support of the children (if any), for division of the property, and for your support, if needed, I would advise you to decline to sign any documents that he has prepared. Remember that your husband's attorney represents only your husband, and has no duty to protect your interests.
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.