I can only answer for myself:
Loving myself means being accepting of myself, warts and all. It means being real with myself. Knowing that I, just like everyone else, have both strengths and flaws, successes and challenges. Loving myself means admitting that I am not perfect and accepting that it is okay-- that no one is perfect. Loving myself means being real, not glossing over my inadequacies, but doing the work to better myself (or make myself feel better), knowing it's not easy, knowing that some things really stink, that I make mistakes and wish that I could do it over again-- but striving to do better next time.
Loving myself means being kind to myself as I see signs of aging, accepting that my body can be 'worked on' (exercise, diet) but will likely never be that hourglass shape it used to be. Can I be honest? Loving ourselves is HARD some days. Silly me, yesterday I realized that I am now that 'rectangle' body shape that I was hoping I wouldn't become-- and I was so bummed out about it feeling so bad about myself.... but part of loving one's self (for me, anyway) is feeling sorry for myself for a day and then getting back on the horse, getting back to doing what makes me feel good in my body. Today I've walked three miles and met a friend I adore for coffee because it makes ME feel good. Not because I might lose weight or wear a cuter dress at the holiday party-- but because it nurtured my soul to be out in this sunny, crisp gorgeous autumn morning.
Loving oneself also sometimes means doing some very, very hard work, digging through the past and sorting out the old, bad messages I received-- those damaging moments which informed me that I wasn't good enough, pretty enough, *anything* enough. Some of us live through parenting as children which truly destroyed our self-esteem, even if the parents we had were 'well-meaning' or not-- stuff happens. For my individual path, loving myself has only come in the last 10 years or so, when I was finally able to gain ground on the past and see that I wasn't a bad person, just had a bad situation handed to me early on. For some of us, being Okay with ourselves is counter-intuitive to how we have been raised. A lot of growth has to happen before we can go forward with love, in love, for ourselves and for others. When we allow someone to empathize with us, with our struggles, when we forgive ourselves for the mistakes we've made and learn that knowing better and doing better are small changes we make, not always huge, dramatic Oprah Winfrey type revelations.
When we can accept ourselves as having value, just for being, period. I think that is a great moment when we can do this without comparing ourselves to anyone else. That my creative pursuits/expressions- in writing, cooking, how I keep my house and garden, how I help my son and husband through life... that all of this has value, even if no one else says so-- that it has value to me, for me. Measuring myself up to what I deem to be my best or highest self-- self-love changes how we perceive the world, and, I believe, can help us be more at peace with our world.
I know this is lengthy, and hope some of this is helpful. Overall, self-love is a process of growth, acknowledgement and acceptance.
ETA: tip of the hat to Dawi and Christy Lee-- they both make excellent points!