Both shared the same meaning, "old."
But they were used for different purposes.
"เก่า" will be used when ... 1. you describe how old something is (but you can' say "He is so เก่า," because that is so wrong.). You can only describe a subject, for example: ของเก่า (which means antiques).
"เดิม" will be used when ... 1. you want to describe the oldness of someone or something, in a sense of how familiar it is to you. I can make an example as shown: เจอกันที่เดิม means Let's meet at the same old place (it implies that you and your friends have met at that place before.). Or it could be ไปที่ไหนก็เจอแต่คนหน้าเดิมๆ means Everywhere I go, I only see the old faces (it implies that there are nothing new. It was as usual. No one new. No excitement in life. Bored.)
Hope those explanation helps. :)