Well this is funny that my name here is luvyrself. Loving yourself first means that you have healthy self esteem, eg confidence in yourself so that you dont feel like a black hole without a significant other. You might have great respect for yourself yet still feel lonely,but you still enjoy life when you are alone.
The reason this comes up all the time is that when we go into a relationship without a healthy regard for ourselves, our lack of self esteem is likely to hurt the relationship, eg suck the life out of it,create problems.
We cant always choose what order our needs will be met in life. Sometimes we might meet a partner before we have a career or some other kind of fulfillment, but I think things go much more smoothly in a relationship when we are first more fulfilled on our own.