When God called Abraham to come out of Ur, Abraham obeyed and respected God's calling. He went into a land he did not know and where he did not know anyone.
He showed loyalty and faithfulness to God by believing in Him though his culture really doesn't support that belief. He also continued to be loyal to Him even when it took so long before God's promise to him of having his own son was fulfilled. And when he was tested and asked to offer up his only son Isaac, he showed his loyalty and faith to God by doing as he was told.
In Abraham's journey of faith, he never left or turned his back on God. For me, that is true loyalty and respect towards God.