About how much memory does the human brain have?

Like, for example, if I record a 10 minute video on my iPhone, then there's like absolutely no room for me to take any more pictures. However, with our brains, we're basically recording video 24/7, right?!

Technically speaking, the capacity of long term memory is infinite. A simple model to help understand why most people don't remember the majority of what they experience is the modal model of memory (Atkinson and Shiffrin 1968). There are three memory stores: the sensory store, the short term memory store, and the long term memory store. Everything that comes in from your senses is very briefly (about 1/20th of a second for visual input and a few seconds for auditory input) stored in the sensory store. To go from the sensory store to the short term memory store, attention is (most of the time) needed--the rest of the input is lost forever. In the short term store, memories can last for about 15-30 seconds. The short term memory store is actually quite complex (feel free to look up Baddeley s working memory model to understand the components), but for this explanation, all you need to know is that you can keep memories in your short term memory and eventually move them into long term memory by (1) repeating the phrase, list, etc. In your mind, which is known as maintenance rehearsal, or (2) tie the memory to a bigger whole, different concept, deeper meaning/context, etc. To help memories go into the long term memory. This is called elaborate rehearsal. An example of this elaboration is remembering a word by connecting it to a picture, like the work "facebook" with a mental image of a book with faces in it. The rest of the memory not rehearsed is lost. Again, the process is more complicated than this because the short term memory store consists of multiple systems, but explaining them here would be unnecessary and confusing. Anyway, the last store is the long term memory store, where all of the memories encoded from the short term memory store end up. The capacity is infinite, as the brain does not really "grow" when you make memories, but rather folds in on itself to increase brain surface area. Memories in the long term memory can last a lifetime, but sometimes fade away when they are not retrieved into the short term memory to be thought about (because consciousness exists in the short term memory, again this is derived from the more specific working memory model).
Hope you learned something today and hope this helped.
-George