# who had a reputation as pillars

"who were known to be important leaders of the church". Pillars are posts that support a building. Here it refers to important leaders. 

# recognized the grace that had been given to me

"recognized the grace that God had given to me" 

# gave the right hand of fellowship to Barnabas and me

"welcomed Barnabas and me as fellow workers" or "welcomed Barnabas and me with honor". Grasping and shaking the right hand was a symbol of fellowship.