A request for “admissions of fact" is a list of short sentences which include facts which the opposing party is required to respond to. This list may be served upon the opposing party and any other party you feel has pertinent information in the same way interrogatories are. For example, if you state allows divorce on the grounds of adultery, you may send a request for admissions of facts to your spouse and the other man/other woman. If you suspect the parties were together on certain dates and times you can request they admit to that fact.
If the opposing party fails to respond within 30 days it is consider to be the same as an admission of the fact or facts. State laws vary regarding rules of civil procedure for admissions of fact. Research you state’s civil procedures and rules for how to serve a request for admissions of fact.