Wobbly front tire help

So I've never been anything more than a casual bike rider (and probably never will be). I haven't had a bike for years and actually just got a free one from my sister. The problem is, there is a tiny wobble in the front tire. Not enough that you can't ride it, just that it's annoying.

I know nothing about bikes beyond how to get on them and change the gears or get the chain back on if it comes off :). Do you guys have any tips or ideas on things I can research to try and fix it? I just moved to a house that has an awesome trail literally across the street and I've already been out riding it a couple times.

I don't know if this really helps, but here is a video I tried to take to illustrate the issue. Let me know if I can provide any more info.

https://www.dropbox.com/s/cjxrhg7r7o6gboy/2017-06-25%2021.51.14.mp4?dl=0