It is a warning from your landlord. A landlord who believes you have broken (breached) a major (substantial) rule in your lease, other than not paying rent, may give you this type of notice.
The notice should tell you exactly which important ("material") part of the rental agreement the landlord believes you are breaking. You then have 10 days from the date you got the notice to stop breaking the rules.
Example: Your lease states that people who are not listed on the lease cannot stay with you for more than one week. Your landlord might give you a 10-Day Notice, stating you have "unauthorized occupants." You then have 10 days for your unauthorized guest to leave, or your landlord may file an eviction lawsuit against you.
The landlord must win an eviction lawsuit against you and get a judge to sign an order directing the sheriff to evict you.
If you fix the problem within 10 days of getting the notice, your landlord should stop the eviction process.