It means "after doing 〜". Almost like
- 両親とよく相談した上で、留学することにした。 → After discussing it with my parents, I decided that I'll study abroad.
- 家を買う場合は、十分調べた上で、決めた方がいい。 → When you buy a house, you should choose (it) after doing sufficient research.
- よく考えた上で、返事をするつもりだ。 → I intend to reply after careful consideration.
There is some other nuance I believe, but I'll have to look it up later. The nuance to it is that the second action is performed based on the result of the first action (as @TokyoNagoya mentioned). With
〜てから, no such relationship is required, meaning that it simply indicates temporal order. For example
○ 昼食を食べてから銀行に行く → "I'll go to the bank after I eat lunch" → Going to the bank doesn't depend on me eating lunch; simply states the order of what I'm doing.
?/× 昼食を食べた上で銀行に行く → It introduces a dependency for going to the bank on eating lunch. Almost like "As a result of eating lunch, I'll go to the bank." Doesn't make much sense.