In your sentences, you have used a compound subject--reading and understanding. The problem is that subject/verb identification and/or agreement probably isn't quite clear to you. Your subject in both sentences is:
- reading and understanding
This is a compound singular noun subject. Since it is singular, it must take a singular verb, and a singular verb will take the "s" form. A plural noun would take a plural verb, which would not take the "s" form unlike a plural noun which would require an "s" form.
- a dog/barks
- the dogs/bark
So your sentence "Reading poems and understanding them has always been easy for me," would be the correct sentence.
The first is correct.