Blepharitis: can be an acute or chronic condition affecting the eyelid margins. If the normal oil glands become clogged or functions poorly the oil backup will irritate of the lid margin. The irritated margin becomes inflamed and can become infected. If you have trouble with red irritated eyelids the initial approach is to improve oil gland function and remove any irritants. This may require stopping eye make-up, warm compress and eye lid massage to encourage healthy oil gland function. Sometimes antibiotic eye drops, or ointment are required to treat this condition.
Here is another interesting article about Blepharitis from the American academy of ophthalmology.