I do cancer diagnostics for a living, look at pap smears the majority of my day, so here's my explanation of what your pap results mean:
ASCUS - means you had some atypical cells on the pap, but not enough of them to determine what they actually mean. Further testing should be done to see if there is an actual lesion, or if they were just very reactive cells. usually they will order an HPV test to confirm if high risk HPV is present or absent. If positive, they will follow up accordingly with a colposcopy to view the cervix and see if any lesions are present.
LSIL - means you have a low-grade lesion. This is the first lesion in the progression towards cervical cancer. They don't always do anything with this diagnosis. Sometimes they will just watch the patient closely to see if it resolves itself, as many LSILs will resolve on their own. If you also test positive for high risk HPV, they would be more likely to do a biopsy to confirm its only LSIL, and make sure HSIL is not present. Will continue to monitor either way for it to resolve itself. Usually continued monitoring means coming in more often for paps, maybe 2x a year rather than once a year until they return to normal for several consecutive paps.
HSIL - this means a high grade lesion is present. There are 3 stages to high grade: moderate, severe, and carcinoma in situ (cancerous cells that are still contained within the cervix, not invasive). High risk HPV is nearly guaranteed to be the cause, as most HSILs are caused by high risk HPV (the leading cause of cervical cancer. HPV inserts itself into cervical cells, causing mutations that develop into lesions, and then later cancer). HSIL diagnosis requires follow up treatment, which at minimum will be a colposcopy to view cervix, and usually involves biopsy removal of the lesion. The good news is that HSILs are still fully contained on the cervix, so can be fully/completely removed and typically patient goes back to normal results following complete removal. This is usually done with a cone biopsy or a LEEP biopsy (cone means they remove a cone shaped section of the cervix to completely remove the lesion, LEEP means they use a loop excision tool to remove the lesion). Yes, I realize it can be a scary process to go through, but this is why cervical cancer screening is SOOO effective. Catching these precancerous lesions, and being able to completely remove them means they won't further develop into cancer later. They will be gone. Removed. Cervical cancer rates have decreased significantly in developed countries because of this.
Cervical cancer - malignant cells are present, and have broken through the basement membrane to become invasive. Typically treated with hysterectomy to remove cancerous cells. Again, if caught early, very treatable with hysterectomy if cancer still confined to that area. This diagnosis is extremely rare in this day and age, honestly, as most women are getting screened regularly, and pre-cancerous lesions are caught, followed, or treated/removed to prevent getting to this point.
I hope this helps you understand it a little better, and puts your mind more at ease. I know it always makes me feel better to know more about something, so I don't feel so in the dark about it. Please don't think the worst of this diagnosis; I'm sure your doctors will take great care of you and make sure to follow up however needed to ensure you return to normal paps.