Many times obstacles are both. The example of the maze in the Triwizard Tournament in Goblet of Fire is a good example. The maze was a physical impediment to the goal of winning the cup. Harry overcoming his jealousy of Cedric was an internal accomplishment.
As in real life, when characters overcome obstacles, they grow. This is the crux of character development. Character development is not what you, the author, write out as descriptions of your character. Character development occurs when your character, through the plot of your story, makes choices, right or wrong, and changes because of it. When you look at a character from the beginning to the end of a story and see this change, it should be dramatic and noticeable and is called a character arc or growth arc.
We're all familiar with Harry's overall series growth arc. He goes from being an unloved orphan stuffed away in a closet to the celebrated savior of the magical world. Along the way, he must overcome many obstacles to obtain the maturity, skill, and wisdom to defeat the darkest wizard of all time.
Each book presents its own set of obstacles and challenges that Harry must face. Some of these obstacles are external--such as Snape's hatred, Dumbledore's slowness to reveal crucial information, and Voldemort's increasing shenanigans to do Harry off. Other obstacles are internal--Harry's lack of belief in his own powers coupled with his lack of knowledge of the wizarding world and what happened in Godric's Hollow. Internal conflicts also include his inability to trust in the manner of Dumbledore and his disbelief that love is more powerful than hatred.
Most writers understand the importance of carefully plotting their protagonist's growth arc. They'll spend much time and energy charting their hero's GMC, torturing their heroine, and assuring that the turning points are strong and powerful. However, the strength of a truly good novel often rests in how much energy the author puts into developing their secondaries as well.
For example:
Character | Beginning Situation | Obstacle to Overcome | Ending Triumph |
Dobby | Enslaved to the Malfoys | Cannot act on his own against Malfoys without punishing self | Due to his loyalty to Harry, wins his freedom when Harry slips Mr. Malfoy the sock. |
Ginny | Crush on Harry, though he doesn't notice her | Tongue-tied around Harry | Increased strength and self-confidence through other relationships. Dates/marries Harry. |
Ron | Youngest son with five older brothers | In shadows of brothers, in shadow of Harry | Overcame his fears of living in shadows and returned to his best friends. Achieved greater fame than any of his brothers by helping to defeat Voldemort. |
Neville | Living with grandmother, who belittles him. Unpopular at school. | Poor memory, inept, lack of confidence | Showed the power of his magic in killing the last Horcrux, the one closest to Voldemort, his snake. |
Snape | Hates Harry. Not the most trusted professor. | Poor decisions in past, hurt the one he most loved | Helped to save the life of Lily's son and restore the Wizarding World. |
Throw obstacles into the path of your characters. Challenge them to new heights with the problems they must overcome. Don't ever let their way be too easy. Otherwise, who does the reader have to cheer for?
Remember the power of the underdog. Everyone cheers when the underdog wins out against tremendous odds. But when even an underdog is not challenged, or fails, he remains an underdog that no one cares about or remembers.