You're right; not everyone believed in Jesus during His time on earth, although they saw His miracles and heard His teaching. Many did believe -- but others didn't, and some of them even turned against Him and urged the authorities to put Him to death.
Why didn't they believe? For the same reason some people today don't believe, although they've heard the Bible's message that God loves them, and that Christ died to give them new life, both now and forever. The problem is inside of us -- in the stubbornness of our hearts and wills. We want to run our own lives -- and we know that if we yield ourselves to Christ, we can't keep on living the way we once did. Like the rebellious men in one of Jesus' parables, we declare, "We don't want this man to be our king" (Luke 19:14).
In reality, of course, people today come up with all kinds of excuses not to believe in Jesus or yield their lives to Him -- just as they did in Jesus' time. Pride . . . a particular sin . . . doubt . . . peer pressure . . . these and countless other excuses keep Jesus out of our lives. But it doesn't have to be that way, because He alone offers us lasting hope in the midst of a world of despair and sin.
Don't let these things -- or anything else -- keep you from Christ. Instead, realize who He is and what He has done for you by His death and resurrection. Then by faith open your heart and life to Him. "Then you will know the truth, and the truth will set you free" (John 8:32).