Yamanote Line is a looped train service. If you board a train at a Yamanote-station and stay inside for an hour, you will be able to alight at the same train station. Now, trains on the Inner Loop move anticlockwise. If you start at Tōkyō Station, you will be at Ikebukuro Station in 15 minutes, at Shinjuku after another 15 minutes, and at Shinagawa after three quarters of an hour since Tōkyō, and finally be back there in one hour. The Outer Loop travels from Tōkyō to Shinagawa, to Shinjuku and Ikebukuro until it comes back to Tōkyō.
It must be noted that inner and outer refers to the physical placement of the train tracks. It makes sense in a country where lefthand-side traffic is the norm.
N.B.: 内回り (Inner Loop) and 外回り (Outer Loop) are official terms, not Ms. Yu's literary coinage.