When we read EEG's, we look at your brain waves. The "background rhythm" is the wave frequency that your brain is normally at when you're eyes are closed but you're fully awake. Based on the frequency of your brainwaves, they may be classified as beta (>12 waves per second), alpha (8-12 waves per second), theta (4-7 waves per second), or delta (< 4 waves per second). The normal background rhythm should be in the alpha frequency range. Your's was 10-11, which is normal. The amplitude of the brainwave is typically in the 10-20 microvolt range. Your amplitude was essentially normal.
"Artifact" refers to anything that makes it difficult to properly interpret a study. For example, your EEG has "muscle artifact." When muscles (in this case, muscles on your scalp, such as the temporalis muscle) contract, they cause areas of dark squiggly lines on the EEG that have a much higher frequency than your brain in its normal state could ever achieve. Because of muscle artifact, it is sometimes difficult to tell if there are any seizure-type discharges on an EEG. It's common to see muscle artifact when people are chewing, when they are tense, or when they're moving their head or facial muscles a lot.
"Wickets" are normal variants of EEG wave forms. They do not signify any pathology. In the early days of EEG interpretation, people occasionally noticed certain wave forms that seemed to occur in several patients; and it was thought that they must represent some sort of pathology. Subsequently, it was determined that many such wave forms are not "abnormal" but rather are "normal variants." (There are at least half a dozen normal variants that decades ago were thought to possibly represent something pathological but have since been proven to be benign.)
Your EEG shows slower-than-normal wave forms periodic in the temporal lobe region of the brain (e.g. around the area above your ear). This can be due to several things. A structural lesion, such as a tumor, infection, or stroke, could cause such a pattern. It could also be seen in someone who has seizures (particularly when they're just coming out of a seizure). It can also be due to migraine headache. It's noteworthy that you have migraine headaches in that regard.
The EEG report says there is "no epileptiform activity." This means that there is no evidence anywhere in the recording of wave forms that would be indicative of a seizure disorder. A 24-hour EEG has very high sensitivity for picking up evidence of a seizure disorder. That your's showed no such evidence leads them to conclude that you do not have a seizure disorder and that your spells captured on EEG are not seizures.
It is not at all uncommon to see people have spells that can be confused for seizures. In fact, around 30 - 50% of people admitted to epilepsy monitoring units for evaluation for seizures are found to have spells that are, in fact, not seizures. These spells are often referred to as "pseudoseizures," though I personally do not like that term, because it often confuses patients and leads them to believe they have seizures (because "seizure" is part of the word "pseudoseizure") when they actually do not. I prefer the term "nonepileptic spell," (which specifically denotes that it is not a seizure). Nonepileptic spells are very often (i.e. usually) due to psychological stressors. This can be anything from current financial or family troubles to a history of abuse as a child. In fact, between a third and a half of patients with nonepileptic spells have a history of some form of abuse. (Note: That leaves at least 50% who have other psychological stressors.) Sometimes when people experience psychological stress, the subsconscious mind manifests it as a physical symptom (e.g. an apparent seizure or an apparent stroke, apparent blindness, etc.) because that is easier emotionally to deal with than the actual stressor. Often, patients aren't even aware of what the psychological stressor might be. (I have heard many say "But everything is going great in my life right now." When I delve deeper, I often find current or very distant sources of psychological stress that may be at the root of their spells.) Thus, when EEGs that capture such events show them not to be related to seizure, neurologists generally recommend that patients seek a psychologist (or the neurologist may make an appointment with one for the patient) to help identify and deal with whatever the underlying psychological stressor is.