The verses are speaking of Abraham, Sarah, Issac and Jacob in the context of the great chapter of faith in Hebrews 11. It is referring to their obedient faith in following God, no matter what the cost. Because of faith, which was revealed by their obedience, God said that He was not ashamed to be their God. That is an amazing thing to have said about someone. Of course, most of us would say "Sure God is not ashamed to be my God. I go to church, pray some, read His word some, tithe, etc." While all those things are great and godly from a right attitude/motive but that is no reason for God to be proud to be our God, because there are some many lost people doing those things while thinking God is proud to be called their own. Abraham and the others were commended by God for their complete self-denial and total (besides a few flops -it's a given) submission in all things to God Himself. I would ask you to ask yourself "Is God ashamed or proud to be called your God?" Don't just ask yourself, ask God over and over if He is ashamed or not to be called your God. It is not an easy thing to do but an important and necessary discipline for spiritual maturity.
"For whoever is ashamed of Me and My words, the Son of Man will be ashamed of him when He comes in His glory, and the glory of the Father and of the holy angels." - Luke 9:26