Spiders have various spiritual meanings. I used to be frightened by them until I started to look at their symbolism. From what I learned, if you see them often it is time to sit back and reflect on your life. Is something bothering you? Do you feel stuck in an upsetting or uncomfortable situation? Do you feel caught in some ones web? Are you happy with the life you have woven for yourself?
You do not have to answer the questions here. But do take time to reflect on them. Also do not feel bad for killing one. We all do at times, mostly without knowing. Rolling over in bed, moving furniture and sometimes swallowing them in our sleep (Ick!).
At one point I had a hidden sack of eggs in my bedroom. It hatched and the whole apartment was covered. After that I started noticing spiders everywhere I went, and dreaming of them. Some would call it coincidence. Others would say not. I looked them up and reflected on my life. Now I welcome every spider I see, and revel in the knowledge and awareness it offers. The spider may not come to you for a specific reason. However I feel we notice these things when our subconscious mind is trying to bring something to a conscious level ;)