One analogy that I find useful when explaining self-care to clients is to use the 'oxygen mask' analogy. When you travel on an airplane, if there is an incident of low cabin pressure, the flight attendant will instruct you to put your own oxygen mask on yourself before you try and help others put their mask on. The reason for this is that if you try and help someone else get their mask on before you put yours on, there is a possibility that you could both pass out from lack of oxygen. If, however, you first put your mask on yourself, you are then able to focus on helping others who may need your help.
Similarly, we all have 'oxygen masks' in our own life. Our oxygen masks are our energy, time, and resources. If we fill our own tank first, we then have the ability to use our reserves to help other people. If we take care of ourselves by making sure we are doing things to make sure that we have enough energy by eating, sleeping, and exercising, we will have enough energy left over to give to other people. If we take care of ourselves by crafting the time in our days in such a way that we are not over-scheduled, we will have pockets of time available for other people. If we take care to only decide to say 'yes' to the things we really want to and can safely fit into our lives, we are using our resources wisely and we will have enough to spare for others.
If you try and take care of others' needs before your own, you may find that you don't have enough in your 'bank' to give to others. You may deplete your tank by tending to others' needs first before your own, and then in the end you are no good to either yourself or the other person. Self-care is about taking care of yourself first. It does not mean that you do not care about others; quite the contrary. By making an effort to take care of yourself first, you are ensuring that you can care for others.