Limits of piecewise functions - Calculus A/B | Question on finding one sided limits

I've been looking for a place to post this, but it's not really clear where I can get help with this. Hopefully, this is the right spot. 

My question is this. From the screenshot above, why do we have to find one-sided limits? 

-3 is clearly not greater than itself ... so shouldn't we just use the first equation to find the limit? 

Side question: If x=-3+ , I'm not sure how to determine which equation would be from the right vs left. The video didn't go into detail in how to determine this.