It means that since you can't win every argument, or solve every problem, you should not try to win every time (especially for problems/arguments that are relatively small compared to others).

It means that you don’t have enough time/energy/power/money to struggle against everything that you would like to change. So, you have to make smart decisions about what things you want to try to change, and what things you decide just to live with. Often, the phrase is used when a particular battle would involve challenging somebody with a lot of power, such that it might be wise not to challenge that person.

I have a funny story about "picking your battles." One day, my four year old son told us he wanted to eat a peanut butter and jelly and tuna fish sandwich. We were surprised because this is a very strange combination of foods (nobody puts tuna fish into this kind of sandwich). My husband told my son, "No, we are not making that. It is disgusting." My son became more insistent, "I want a peanut butter and jelly and tuna fish sandwich!!!" And my husband kept telling him, "No!" They were both getting more and more upset. I said to my husband, "Let's just make him the sandwich. If it doesn't taste good, he will learn that. If it does taste good to him...well, there is no harm. The food is still healthy and it won't make him sick." So I made my son the strange sandwich and he looked content while he ate it. He only asked for this strange sandwich one more time and then never again. Afterwards, I told my friends, "As a parent, you have to choose your battles." (or maybe I said "pick your battles", they mean the same thing). With a young child, it is natural that there will be disagreements. They are often about important things, so you must be firm and make the child do as you say at those times. But when the disagreement is about something small and unimportant, then maybe it is OK to decide not to fight about it and to let the child have their way. This can help to keep the relationship more peaceful and it saves your energy for you to use in the more important conflicts.

To chose not to participate in minor, unimportant, or overly difficult arguments, contest, or confrontation, saving one's strength instead for those that will be of greater importance or where one has greater chance of success.

Parents often use this expression. You cannot correct your child every time they make a mistake. You have to "pick your battles". Take your stand on the important issues and let minor issues pass. Hope this helps