While there is not a known physical limit to human memory (e.g., as with a computer), there are limitation to memory. There are three levels of memory short-term, long-term, and sensory memory. Short-term memories may be lost if they are not incorporated into long-term memory because the information is not fully understood or given much attention in the first place. This is referred to as encoding failure and the information is forgotten.
Long-term memory has the longest duration and the greatest capacity, but long-term memories can be lost if they remain dormant for extended lengths of time. Also, new information that is stored into long-term memory can interfere with previously stored information in a process called distractive interference. Sensory memories have the shortest duration. It is the ability to retain impressions of sensory information for a few seconds after the original stimulus has ceased.
So, although theoretically there is no know, measurable limit to how much information can be stored in the human mind, there are limitation as far as forgetting and recalling information.
Hope this helps!