I drew this in my religious phase, which happens every few months. I'm on a very normal cycle. For the curious: the last few months has been a severe downturn in belief.
The following argument thumbnail could have been better written and organized. Come to think of it, most of my writings can be better written and organized. You'll have to take what I give you, however.
This was the answer my rabbi gave for the meaning of life: connecting with the infinite. It sounded very profound when he said it. In brief, if there's an infinite being out there that created us, then the best possible explanation for our existence is that we're given an opportunity in this life to grow closer to the infinite.
 An infinite being itself contradicts our existence. By (human) definition, nothing can coexist with infinity since infinity includes everything, including us. There cannot be anything outside of the infinite. There are certain touchpoints in Judaism where the rabbis hold up their hands and say, this is an inherent contradiction of life, and humans will never be able to understand it, regardless how smart or wise we become.
 I'm not a proponent of Intelligent Design. I can very easily imagine a universe created by an infinite being that includes evolution from the galactic down to the organism scale. I even like the idea: the infinite being created the mind-boggling huge universe to show humans a perspective on their existence as compared to infinity (and this is true even if the universe isn't technically infinite--it is as close to infinity as we can understand in a non-mathematical sense).
 By "best explanation," I'm also including the assumption that the infinite being is Good. This isn't technically necessary for this argument, but does help understand why the infinite being would want us to connect to the infinite being.
 Remember, an infinite being doesn't need anything from humans. There is nothing that a human can give an infinite being that it doesn't already have. A perfectly good infinite being would give us something, however. Usually people say existence is the gift. While existence is definitely part of the gift, it can't be the end in itself. The evidence that there needs to be more than existence is in our very makeup: we always ask about the meaning of our lives. Is it really just about feeding our physical body and needs, or is there something greater.
There are rationalist that say the greater meaning in this random world is to make our lives and our children's lives better. I understand and sometimes feel that that is sufficient. Other time, I look to a more spiritual answer. I'm not saying the above is the correct one, but from a logical perspective, it does have its merits.